SET007 Axioms: SET007+784.ax


%------------------------------------------------------------------------------
% File     : SET007+784 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Semilattice Structure of Mizar Types
% 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    : abcmiz_0 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  172 (   6 unit)
%            Number of atoms       : 1558 ( 116 equality)
%            Maximal formula depth :   28 (   9 average)
%            Number of connectives : 1568 ( 182 ~  ;   1  |; 863  &)
%                                         (  35 <=>; 487 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   76 (   1 propositional; 0-3 arity)
%            Number of functors    :   60 (   6 constant; 0-6 arity)
%            Number of variables   :  491 (   0 singleton; 467 !;  24 ?)
%            Maximal term depth    :    5 (   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(cc1_abcmiz_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A) ) ) ) )).

fof(cc2_abcmiz_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v1_abcmiz_0(A) ) ) ) )).

fof(cc3_abcmiz_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_abcmiz_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_yellow_0(A)
          & v1_abcmiz_0(A) ) ) ) )).

fof(cc4_abcmiz_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v1_abcmiz_0(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_yellow_0(A)
          & v1_abcmiz_0(A)
          & v2_abcmiz_0(A) ) ) ) )).

fof(rc1_abcmiz_0,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_abcmiz_0(A)
      & v2_abcmiz_0(A) ) )).

fof(fc1_abcmiz_0,axiom,(
    ! [A] :
      ( ( v1_abcmiz_0(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_rewrite1(u1_orders_2(A)) ) ) )).

fof(rc2_abcmiz_0,axiom,(
    ? [A] :
      ( l1_abcmiz_0(A)
      & v3_abcmiz_0(A) ) )).

fof(rc3_abcmiz_0,axiom,(
    ? [A] :
      ( l1_abcmiz_0(A)
      & v3_abcmiz_0(A)
      & ~ v4_abcmiz_0(A)
      & v5_abcmiz_0(A)
      & v6_abcmiz_0(A) ) )).

fof(fc2_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v4_abcmiz_0(A)
        & l1_abcmiz_0(A) )
     => ~ v1_xboole_0(u1_abcmiz_0(A)) ) )).

fof(rc4_abcmiz_0,axiom,(
    ? [A] :
      ( l2_abcmiz_0(A)
      & v7_abcmiz_0(A) ) )).

fof(fc3_abcmiz_0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B)) )
     => ( ~ v3_struct_0(g2_abcmiz_0(A,B,C,D,E))
        & v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) )).

fof(fc4_abcmiz_0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(B)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B)) )
     => ( ~ v4_abcmiz_0(g2_abcmiz_0(A,B,C,D,E))
        & v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) )).

fof(rc5_abcmiz_0,axiom,(
    ? [A] :
      ( l2_abcmiz_0(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_abcmiz_0(A)
      & v2_abcmiz_0(A)
      & ~ v4_abcmiz_0(A)
      & v5_abcmiz_0(A)
      & v6_abcmiz_0(A)
      & v7_abcmiz_0(A) ) )).

fof(rc6_abcmiz_0,axiom,(
    ? [A] :
      ( l2_abcmiz_0(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_abcmiz_0(A)
      & v2_abcmiz_0(A)
      & ~ v4_abcmiz_0(A)
      & v5_abcmiz_0(A)
      & v6_abcmiz_0(A)
      & v7_abcmiz_0(A)
      & v8_abcmiz_0(A)
      & v9_abcmiz_0(A)
      & v10_abcmiz_0(A) ) )).

fof(fc5_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_abcmiz_0(A)) )
     => ( v1_waybel_0(k3_abcmiz_0(A,B),A)
        & v12_waybel_0(k3_abcmiz_0(A,B),A) ) ) )).

fof(fc6_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) )
     => ( v1_waybel_0(k4_abcmiz_0(A,B),A)
        & v12_waybel_0(k4_abcmiz_0(A,B),A) ) ) )).

fof(fc7_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_abcmiz_0(A)) )
     => ( ~ v1_xboole_0(k7_abcmiz_0(A,B,C))
        & v1_relat_1(k7_abcmiz_0(A,B,C))
        & v1_funct_1(k7_abcmiz_0(A,B,C))
        & v1_finset_1(k7_abcmiz_0(A,B,C))
        & v1_finseq_1(k7_abcmiz_0(A,B,C)) ) ) )).

fof(rc7_abcmiz_0,axiom,(
    ? [A] :
      ( l3_abcmiz_0(A)
      & v11_abcmiz_0(A) ) )).

fof(rc8_abcmiz_0,axiom,(
    ? [A] :
      ( l3_abcmiz_0(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_abcmiz_0(A)
      & v2_abcmiz_0(A)
      & ~ v4_abcmiz_0(A)
      & v11_abcmiz_0(A) ) )).

fof(rc9_abcmiz_0,axiom,(
    ? [A] :
      ( l3_abcmiz_0(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_abcmiz_0(A)
      & v2_abcmiz_0(A)
      & ~ v4_abcmiz_0(A)
      & v5_abcmiz_0(A)
      & v6_abcmiz_0(A)
      & v8_abcmiz_0(A)
      & v9_abcmiz_0(A)
      & v10_abcmiz_0(A)
      & v11_abcmiz_0(A)
      & v12_abcmiz_0(A)
      & v13_abcmiz_0(A)
      & v14_abcmiz_0(A) ) )).

fof(d1_abcmiz_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_abcmiz_0(A)
      <=> v1_rewrite1(u1_orders_2(A)) ) ) )).

fof(d2_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_abcmiz_0(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_hidden(C,B)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & r2_orders_2(A,C,D) ) ) ) ) ) ) )).

fof(d3_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_abcmiz_0(A)
      <=> ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & l1_orders_2(A)
          & v1_abcmiz_0(A) ) ) ) )).

fof(t1_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( r1_yellow_0(A,B)
            & r2_hidden(k1_yellow_0(A,B),B) ) ) ) )).

fof(d4_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ( v4_abcmiz_0(A)
      <=> v1_xboole_0(u1_abcmiz_0(A)) ) ) )).

fof(t2_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ! [B] :
          ( l1_abcmiz_0(B)
         => ( ( u1_abcmiz_0(A) = u1_abcmiz_0(B)
              & v4_abcmiz_0(A) )
           => v4_abcmiz_0(B) ) ) ) )).

fof(d5_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => k1_abcmiz_0(A,B) = k1_funct_1(u2_abcmiz_0(A),B) ) ) )).

fof(t3_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ! [B] :
          ( l1_abcmiz_0(B)
         => ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
           => ! [C] :
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_abcmiz_0(B))
                   => ( C = D
                     => k1_abcmiz_0(A,C) = k1_abcmiz_0(B,D) ) ) ) ) ) ) )).

fof(d6_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ( v5_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => k1_abcmiz_0(A,k1_abcmiz_0(A,B)) = B ) ) ) )).

fof(d7_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ( v6_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => k1_abcmiz_0(A,B) != B ) ) ) )).

fof(t4_abcmiz_0,axiom,(
    ! [A,B] :
      ( A != B
     => ! [C] :
          ( l1_abcmiz_0(C)
         => ( ( u1_abcmiz_0(C) = k2_tarski(A,B)
              & k1_funct_1(u2_abcmiz_0(C),A) = B
              & k1_funct_1(u2_abcmiz_0(C),B) = A )
           => ( ~ v4_abcmiz_0(C)
              & v5_abcmiz_0(C)
              & v6_abcmiz_0(C) ) ) ) ) )).

fof(t5_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ! [B] :
          ( l1_abcmiz_0(B)
         => ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
              & v5_abcmiz_0(A) )
           => v5_abcmiz_0(B) ) ) ) )).

fof(t6_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ! [B] :
          ( l1_abcmiz_0(B)
         => ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
              & v6_abcmiz_0(A) )
           => v6_abcmiz_0(B) ) ) ) )).

fof(d8_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_abcmiz_0(A,B) = k1_funct_1(u3_abcmiz_0(A),B) ) ) )).

fof(t7_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( l2_abcmiz_0(B)
         => ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( C = D
                     => k2_abcmiz_0(A,C) = k2_abcmiz_0(B,D) ) ) ) ) ) ) )).

fof(d9_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ( v8_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ~ ( r2_hidden(C,k2_abcmiz_0(A,B))
                    & r2_hidden(k1_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) )).

fof(t8_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( l2_abcmiz_0(B)
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v8_abcmiz_0(A) )
           => v8_abcmiz_0(B) ) ) ) )).

fof(d10_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
      <=> ( v1_funct_1(u3_abcmiz_0(A))
          & v1_funct_2(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A)))))
          & v20_waybel_0(u3_abcmiz_0(A),A,k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))
          & m2_relset_1(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))) ) ) ) )).

fof(t9_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_abcmiz_0(B) )
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v9_abcmiz_0(A) )
           => v9_abcmiz_0(B) ) ) ) )).

fof(d11_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_abcmiz_0(A,k13_lattice3(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_abcmiz_0(A)),k2_abcmiz_0(A,B),k2_abcmiz_0(A,C)) ) ) ) ) )).

fof(t10_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r3_orders_2(A,B,C)
                 => r1_tarski(k2_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) )).

fof(d12_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k3_abcmiz_0(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,C)
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & D = E
                        & r2_hidden(B,k2_abcmiz_0(A,E)) ) ) ) ) ) ) )).

fof(d13_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k4_abcmiz_0(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ! [E] :
                          ( m1_subset_1(E,u1_abcmiz_0(A))
                         => ( r2_hidden(E,B)
                           => r2_hidden(D,k3_abcmiz_0(A,E)) ) ) ) ) ) ) ) ) )).

fof(t11_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( l2_abcmiz_0(B)
         => ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
           => ! [C] :
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_abcmiz_0(B))
                   => ( C = D
                     => k3_abcmiz_0(A,C) = k3_abcmiz_0(B,D) ) ) ) ) ) ) )).

fof(t13_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r2_hidden(C,k2_abcmiz_0(A,B))
              <=> r2_hidden(B,k3_abcmiz_0(A,C)) ) ) ) ) )).

fof(t14_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r1_tarski(C,k2_abcmiz_0(A,B))
              <=> r2_hidden(B,k4_abcmiz_0(A,C)) ) ) ) ) )).

fof(t16_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => k4_abcmiz_0(A,k1_subset_1(u1_abcmiz_0(A))) = u1_struct_0(A) ) )).

fof(d14_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ( v10_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => ~ v1_xboole_0(k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B)))) ) ) ) )).

fof(t17_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( l2_abcmiz_0(B)
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v10_abcmiz_0(A) )
           => v10_abcmiz_0(B) ) ) ) )).

fof(t18_abcmiz_0,axiom,(
    ! [A] :
      ( ( v8_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => r1_xboole_0(k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B))) ) ) )).

fof(d15_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,k3_abcmiz_0(A,C))
                    & r1_orders_2(A,D,B) ) ) ) ) ) )).

fof(d16_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r1_tarski(C,k2_abcmiz_0(A,D))
                    & r1_orders_2(A,D,B) ) ) ) ) ) )).

fof(t19_abcmiz_0,axiom,(
    $true )).

fof(t20_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_abcmiz_0(A,C,B)
               => ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)))
                  & v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(d17_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => k5_abcmiz_0(A,B,C) = k1_yellow_0(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,C),k6_waybel_0(A,B))) ) ) ) )).

fof(t21_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r3_orders_2(A,k5_abcmiz_0(A,B,C),B) ) ) ) ) )).

fof(t22_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r2_hidden(C,k2_abcmiz_0(A,k5_abcmiz_0(A,B,C))) ) ) ) ) )).

fof(t23_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r2_hidden(k5_abcmiz_0(A,B,C),k3_abcmiz_0(A,C)) ) ) ) ) )).

fof(t24_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_orders_2(A,D,B)
                      & r2_hidden(C,k2_abcmiz_0(A,D)) )
                   => ( r1_abcmiz_0(A,B,C)
                      & r3_orders_2(A,D,k5_abcmiz_0(A,B,C)) ) ) ) ) ) ) )).

fof(t25_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r2_hidden(C,k2_abcmiz_0(A,B))
               => ( r1_abcmiz_0(A,B,C)
                  & k5_abcmiz_0(A,B,C) = B ) ) ) ) ) )).

fof(t26_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_abcmiz_0(A))
                 => ( ( r1_abcmiz_0(A,B,C)
                      & r1_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) )
                   => ( r1_abcmiz_0(A,B,D)
                      & r1_abcmiz_0(A,k5_abcmiz_0(A,B,D),C)
                      & k5_abcmiz_0(A,k5_abcmiz_0(A,B,D),C) = k5_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) ) ) ) ) ) ) )).

fof(t27_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_abcmiz_0(A,C,B)
               => ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)))
                  & v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(d18_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => k6_abcmiz_0(A,B,C) = k1_yellow_0(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,C),k6_waybel_0(A,B))) ) ) ) )).

fof(t28_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) = B ) ) )).

fof(d19_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( D = k7_abcmiz_0(A,B,C)
                  <=> ( k3_finseq_1(D) = k1_nat_1(k3_finseq_1(C),np__1)
                      & k1_funct_1(D,np__1) = B
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m1_subset_1(F,u1_abcmiz_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_hidden(E,k4_finseq_1(C))
                                      & F = k1_funct_1(C,E)
                                      & G = k1_funct_1(D,E) )
                                   => k1_funct_1(D,k1_nat_1(E,np__1)) = k5_abcmiz_0(A,G,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = k12_finseq_1(u1_struct_0(A),B) ) ) )).

fof(t30_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => k7_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k10_finseq_1(B,k5_abcmiz_0(A,B,C)) ) ) ) )).

fof(d20_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => k8_abcmiz_0(A,B,C) = k1_funct_1(k7_abcmiz_0(A,B,C),k1_nat_1(k3_finseq_1(C),np__1)) ) ) ) )).

fof(t31_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = B ) ) )).

fof(t32_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => k8_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k5_abcmiz_0(A,B,C) ) ) ) )).

fof(t33_abcmiz_0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( v4_ordinal2(C)
             => ( r1_xreal_0(np__1,C)
               => ( r1_xreal_0(k3_finseq_1(A),C)
                  | k1_funct_1(k1_rewrite1(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) )).

fof(t34_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] :
              ( v4_ordinal2(C)
             => ( ~ r1_xreal_0(k3_finseq_1(B),C)
               => k1_funct_1(k1_rewrite1(A,B),k2_xcmplx_0(k3_finseq_1(A),C)) = k1_funct_1(B,k2_xcmplx_0(C,np__1)) ) ) ) ) )).

fof(t35_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k1_rewrite1(k7_abcmiz_0(A,B,C),k7_abcmiz_0(A,k8_abcmiz_0(A,B,C),D)) ) ) ) ) )).

fof(t36_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ! [E] :
                      ( v4_ordinal2(E)
                     => ( r2_hidden(E,k4_finseq_1(C))
                       => k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),E) = k1_funct_1(k7_abcmiz_0(A,B,C),E) ) ) ) ) ) ) )).

fof(t37_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),k1_nat_1(k3_finseq_1(C),np__1)) = k8_abcmiz_0(A,B,C) ) ) ) ) )).

fof(t38_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k8_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) )).

fof(d21_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
              <=> ! [D] :
                    ( v4_ordinal2(D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_abcmiz_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r2_hidden(D,k4_finseq_1(C))
                                & E = k1_funct_1(C,D)
                                & F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
                             => r1_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) )).

fof(t39_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) )).

fof(t40_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
              <=> r3_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) )).

fof(t41_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => ( r3_abcmiz_0(A,B,C)
                      & r3_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) )).

fof(t42_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] :
                    ( v4_ordinal2(D)
                   => ! [E] :
                        ( v4_ordinal2(E)
                       => ( ( r1_xreal_0(np__1,D)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(E,k1_nat_1(k3_finseq_1(C),np__1)) )
                         => ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( F = k1_funct_1(k7_abcmiz_0(A,B,C),D)
                                      & G = k1_funct_1(k7_abcmiz_0(A,B,C),E) )
                                   => r3_orders_2(A,G,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t43_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,k2_relat_1(k7_abcmiz_0(A,B,C)))
                     => ( r3_orders_2(A,k8_abcmiz_0(A,B,C),D)
                        & r3_orders_2(A,D,B) ) ) ) ) ) ) ) )).

fof(t44_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => r3_orders_2(A,k8_abcmiz_0(A,B,C),B) ) ) ) ) )).

fof(t45_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => r1_tarski(k2_relat_1(C),k2_abcmiz_0(A,k8_abcmiz_0(A,B,C))) ) ) ) ) )).

fof(t46_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( D = k2_relat_1(C)
                     => r2_abcmiz_0(A,B,D) ) ) ) ) ) ) )).

fof(t47_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( ( r3_abcmiz_0(A,B,C)
                      & r1_tarski(k2_relat_1(D),k2_relat_1(C)) )
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(E,k2_relat_1(k7_abcmiz_0(A,B,D)))
                         => r3_orders_2(A,k8_abcmiz_0(A,B,C),E) ) ) ) ) ) ) ) )).

fof(t48_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) )).

fof(t49_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) )).

fof(t50_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r3_orders_2(A,k6_abcmiz_0(A,B,C),B) ) ) ) ) )).

fof(t51_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r1_tarski(C,k2_abcmiz_0(A,k6_abcmiz_0(A,B,C))) ) ) ) ) )).

fof(t52_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r2_hidden(k6_abcmiz_0(A,B,C),k4_abcmiz_0(A,C)) ) ) ) ) )).

fof(t53_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_orders_2(A,D,B)
                      & r1_tarski(C,k2_abcmiz_0(A,D)) )
                   => ( r2_abcmiz_0(A,B,C)
                      & r3_orders_2(A,D,k6_abcmiz_0(A,B,C)) ) ) ) ) ) ) )).

fof(t54_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r1_tarski(C,k2_abcmiz_0(A,B))
               => ( r2_abcmiz_0(A,B,C)
                  & k6_abcmiz_0(A,B,C) = B ) ) ) ) ) )).

fof(t55_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                 => ( ( r2_abcmiz_0(A,B,C)
                      & r1_tarski(D,C) )
                   => r2_abcmiz_0(A,B,D) ) ) ) ) ) )).

fof(t56_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
                     => ( ( E = k2_xboole_0(D,k1_tarski(C))
                          & r2_abcmiz_0(A,B,E) )
                       => k5_abcmiz_0(A,k6_abcmiz_0(A,B,D),C) = k6_abcmiz_0(A,B,E) ) ) ) ) ) ) )).

fof(t57_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( D = k2_relat_1(C)
                     => k8_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) ) ) ) ) ) ) )).

fof(d22_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_abcmiz_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_abcmiz_0(A),u1_struct_0(A)) )
         => ( B = k9_abcmiz_0(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => k8_funct_2(u1_abcmiz_0(A),u1_struct_0(A),B,C) = k1_yellow_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,C),k3_abcmiz_0(A,k1_abcmiz_0(A,C)))) ) ) ) ) )).

fof(d23_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => k10_abcmiz_0(A,B) = k8_funct_2(u1_abcmiz_0(A),u1_struct_0(A),u4_abcmiz_0(A),B) ) ) )).

fof(d24_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v12_abcmiz_0(A)
      <=> k7_funct_2(u1_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A),u2_abcmiz_0(A),u4_abcmiz_0(A)) = u4_abcmiz_0(A) ) ) )).

fof(d25_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v13_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => ( r2_lattice3(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B))),k10_abcmiz_0(A,B))
              & ~ ( k3_abcmiz_0(A,B) != k1_xboole_0
                  & k3_abcmiz_0(A,k1_abcmiz_0(A,B)) != k1_xboole_0
                  & k10_abcmiz_0(A,B) != k1_yellow_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B)))) ) ) ) ) ) )).

fof(d26_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v12_abcmiz_0(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => k10_abcmiz_0(A,k1_abcmiz_0(A,B)) = k10_abcmiz_0(A,B) ) ) ) )).

fof(d27_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
              <=> ( r1_orders_2(A,B,k10_abcmiz_0(A,C))
                  & r1_abcmiz_0(A,B,C) ) ) ) ) ) )).

fof(d28_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r5_abcmiz_0(A,B,C)
              <=> ! [D] :
                    ( v4_ordinal2(D)
                   => ! [E] :
                        ( m1_subset_1(E,u1_abcmiz_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r2_hidden(D,k4_finseq_1(C))
                                & E = k1_funct_1(C,D)
                                & F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
                             => r4_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) )).

fof(t58_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r5_abcmiz_0(A,B,C)
               => r3_abcmiz_0(A,B,C) ) ) ) ) )).

fof(t59_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r5_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) )).

fof(t60_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
              <=> r5_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) )).

fof(t61_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => ( r5_abcmiz_0(A,B,C)
                      & r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) )).

fof(t62_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( ( r5_abcmiz_0(A,B,C)
                      & r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) )
                   => r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) ) )).

fof(d29_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r6_abcmiz_0(A,B,C)
              <=> ? [D] :
                    ( m2_finseq_1(D,u1_abcmiz_0(A))
                    & k2_relat_1(D) = C
                    & r5_abcmiz_0(A,B,D) ) ) ) ) ) )).

fof(t63_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r6_abcmiz_0(A,B,C)
               => v1_finset_1(C) ) ) ) ) )).

fof(t64_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) ) ) )).

fof(t65_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ~ ( r6_abcmiz_0(A,B,C)
                  & ! [D] :
                      ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                     => ~ ( r1_tarski(D,C)
                          & r6_abcmiz_0(A,B,D)
                          & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D)
                          & ! [E] :
                              ( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
                             => ( ( r1_tarski(E,D)
                                  & r6_abcmiz_0(A,B,E)
                                  & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,E) )
                               => E = D ) ) ) ) ) ) ) ) )).

fof(d30_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v14_abcmiz_0(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_abcmiz_0(A))
                   => ~ ( r4_abcmiz_0(A,B,D)
                        & r3_orders_2(A,k5_abcmiz_0(A,B,D),C)
                        & ! [E] :
                            ( ( v1_finset_1(E)
                              & m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A))) )
                           => ~ ( r6_abcmiz_0(A,k10_lattice3(A,B,C),E)
                                & k6_abcmiz_0(A,k10_lattice3(A,B,C),E) = C ) ) ) ) ) ) ) ) )).

fof(t66_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ~ ( r6_abcmiz_0(A,B,C)
                  & ! [D] :
                      ( ( v2_funct_1(D)
                        & m2_finseq_1(D,u1_abcmiz_0(A)) )
                     => ~ ( k2_relat_1(D) = C
                          & r5_abcmiz_0(A,B,D) ) ) ) ) ) ) )).

fof(d31_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k11_abcmiz_0(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> ? [E] :
                          ( m1_subset_1(E,u1_abcmiz_0(A))
                          & ~ r2_hidden(E,k2_abcmiz_0(A,D))
                          & r4_abcmiz_0(A,D,E)
                          & k5_abcmiz_0(A,D,E) = C ) ) ) ) ) ) ) )).

fof(t67_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => r1_tarski(k11_abcmiz_0(A),u1_orders_2(A)) ) )).

fof(t68_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_rewrite1(k11_abcmiz_0(A),B,C)
               => r3_orders_2(A,B,C) ) ) ) ) )).

fof(t69_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => v2_relat_2(k11_abcmiz_0(A)) ) )).

fof(t70_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => v3_rewrite1(k11_abcmiz_0(A)) ) )).

fof(t71_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( ( r1_tarski(D,C)
                        & r6_abcmiz_0(A,B,D)
                        & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
                     => D = C ) )
               => ! [D] :
                    ( ( v2_funct_1(D)
                      & m2_finseq_1(D,u1_abcmiz_0(A)) )
                   => ( ( k2_relat_1(D) = C
                        & r5_abcmiz_0(A,B,D) )
                     => ! [E] :
                          ( v4_ordinal2(E)
                         => ( ( r1_xreal_0(np__1,E)
                              & r1_xreal_0(E,k3_finseq_1(D)) )
                           => r2_hidden(k4_tarski(k1_funct_1(k7_abcmiz_0(A,B,D),k2_xcmplx_0(E,np__1)),k1_funct_1(k7_abcmiz_0(A,B,D),E)),k11_abcmiz_0(A)) ) ) ) ) ) ) ) ) )).

fof(t72_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( ! [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( ( r1_tarski(D,C)
                        & r6_abcmiz_0(A,B,D)
                        & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
                     => D = C ) )
               => ! [D] :
                    ( ( v2_funct_1(D)
                      & m2_finseq_1(D,u1_abcmiz_0(A)) )
                   => ( ( k2_relat_1(D) = C
                        & r5_abcmiz_0(A,B,D) )
                     => m1_rewrite1(k4_finseq_5(u1_struct_0(A),k7_abcmiz_0(A,B,D)),k11_abcmiz_0(A)) ) ) ) ) ) ) )).

fof(t73_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( r6_abcmiz_0(A,B,C)
               => r1_rewrite1(k11_abcmiz_0(A),k6_abcmiz_0(A,B,C),B) ) ) ) ) )).

fof(t74_abcmiz_0,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ! [C] :
              ( m1_rewrite1(C,B)
             => ( r2_hidden(k1_funct_1(C,np__1),A)
               => m2_finseq_1(C,A) ) ) ) ) )).

fof(t75_abcmiz_0,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( r1_rewrite1(B,C,D)
                 => r2_hidden(D,A) ) ) ) ) )).

fof(t76_abcmiz_0,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( ( v4_rewrite1(B)
              & v2_rewrite1(B) )
           => ! [C] :
                ( m1_subset_1(C,A)
               => r2_hidden(k2_rewrite1(B,C),A) ) ) ) ) )).

fof(t77_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r1_rewrite1(k11_abcmiz_0(A),B,C)
                  & ! [D] :
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A))) )
                     => ~ ( r6_abcmiz_0(A,C,D)
                          & B = k6_abcmiz_0(A,C,D) ) ) ) ) ) ) )).

fof(t78_abcmiz_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v8_rewrite1(k11_abcmiz_0(A))
        & v4_rewrite1(k11_abcmiz_0(A)) ) ) )).

fof(d32_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k12_abcmiz_0(A,B) = k2_rewrite1(k11_abcmiz_0(A),B) ) ) )).

fof(t79_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_rewrite1(k11_abcmiz_0(A),B,k12_abcmiz_0(A,B)) ) ) )).

fof(t80_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_orders_2(A,B,k12_abcmiz_0(A,B)) ) ) )).

fof(t82_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(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_abcmiz_0(A))
                 => ( ( r4_abcmiz_0(A,B,D)
                      & r3_orders_2(A,k5_abcmiz_0(A,B,D),k12_abcmiz_0(A,C)) )
                   => r3_orders_2(A,B,k12_abcmiz_0(A,C)) ) ) ) ) ) )).

fof(t83_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => r3_orders_2(A,k12_abcmiz_0(A,B),k12_abcmiz_0(A,C)) ) ) ) ) )).

fof(t84_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
               => k12_abcmiz_0(A,k5_abcmiz_0(A,B,C)) = k12_abcmiz_0(A,B) ) ) ) ) )).

fof(s1_abcmiz_0,axiom,
    ( ? [A] :
        ( v1_finset_1(A)
        & p1_s1_abcmiz_0(A) )
   => ? [A] :
        ( v1_finset_1(A)
        & p1_s1_abcmiz_0(A)
        & ! [B] :
            ( ( r1_tarski(B,A)
              & p1_s1_abcmiz_0(B) )
           => B = A ) ) )).

fof(s2_abcmiz_0,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => ! [B] :
              ( m1_subset_1(B,f1_s2_abcmiz_0)
             => ( r2_hidden(k4_tarski(A,B),f2_s2_abcmiz_0)
               => p1_s2_abcmiz_0(A,B) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => p1_s2_abcmiz_0(A,A) )
      & ! [A] :
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => ! [B] :
              ( m1_subset_1(B,f1_s2_abcmiz_0)
             => ! [C] :
                  ( m1_subset_1(C,f1_s2_abcmiz_0)
                 => ( ( p1_s2_abcmiz_0(A,B)
                      & p1_s2_abcmiz_0(B,C) )
                   => p1_s2_abcmiz_0(A,C) ) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,f1_s2_abcmiz_0)
       => ! [B] :
            ( m1_subset_1(B,f1_s2_abcmiz_0)
           => ( r1_rewrite1(f2_s2_abcmiz_0,A,B)
             => p1_s2_abcmiz_0(A,B) ) ) ) )).

fof(dt_l1_abcmiz_0,axiom,(
    $true )).

fof(existence_l1_abcmiz_0,axiom,(
    ? [A] : l1_abcmiz_0(A) )).

fof(dt_l2_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ( l1_orders_2(A)
        & l1_abcmiz_0(A) ) ) )).

fof(existence_l2_abcmiz_0,axiom,(
    ? [A] : l2_abcmiz_0(A) )).

fof(dt_l3_abcmiz_0,axiom,(
    ! [A] :
      ( l3_abcmiz_0(A)
     => l2_abcmiz_0(A) ) )).

fof(existence_l3_abcmiz_0,axiom,(
    ? [A] : l3_abcmiz_0(A) )).

fof(abstractness_v3_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ( v3_abcmiz_0(A)
       => A = g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) ) ) )).

fof(abstractness_v7_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ( v7_abcmiz_0(A)
       => A = g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) ) ) )).

fof(abstractness_v11_abcmiz_0,axiom,(
    ! [A] :
      ( l3_abcmiz_0(A)
     => ( v11_abcmiz_0(A)
       => A = g3_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A),u4_abcmiz_0(A)) ) ) )).

fof(dt_k1_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( l1_abcmiz_0(A)
        & m1_subset_1(B,u1_abcmiz_0(A)) )
     => m1_subset_1(k1_abcmiz_0(A,B),u1_abcmiz_0(A)) ) )).

fof(dt_k2_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k2_abcmiz_0(A,B),k1_zfmisc_1(u1_abcmiz_0(A))) ) )).

fof(dt_k3_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( l2_abcmiz_0(A)
        & m1_subset_1(B,u1_abcmiz_0(A)) )
     => m1_subset_1(k3_abcmiz_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) )
     => m1_subset_1(k4_abcmiz_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_abcmiz_0(A)) )
     => m1_subset_1(k5_abcmiz_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k6_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
     => m1_subset_1(k6_abcmiz_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k7_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_abcmiz_0(A)) )
     => m2_finseq_1(k7_abcmiz_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k8_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_finseq_1(C,u1_abcmiz_0(A)) )
     => m1_subset_1(k8_abcmiz_0(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k9_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ( v1_funct_1(k9_abcmiz_0(A))
        & v1_funct_2(k9_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A))
        & m2_relset_1(k9_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A)) ) ) )).

fof(dt_k10_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A)
        & m1_subset_1(B,u1_abcmiz_0(A)) )
     => m1_subset_1(k10_abcmiz_0(A,B),u1_struct_0(A)) ) )).

fof(dt_k11_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => m2_relset_1(k11_abcmiz_0(A),u1_struct_0(A),u1_struct_0(A)) ) )).

fof(dt_k12_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k12_abcmiz_0(A,B),u1_struct_0(A)) ) )).

fof(dt_u1_abcmiz_0,axiom,(
    $true )).

fof(dt_u2_abcmiz_0,axiom,(
    ! [A] :
      ( l1_abcmiz_0(A)
     => ( v1_funct_1(u2_abcmiz_0(A))
        & v1_funct_2(u2_abcmiz_0(A),u1_abcmiz_0(A),u1_abcmiz_0(A))
        & m2_relset_1(u2_abcmiz_0(A),u1_abcmiz_0(A),u1_abcmiz_0(A)) ) ) )).

fof(dt_u3_abcmiz_0,axiom,(
    ! [A] :
      ( l2_abcmiz_0(A)
     => ( v1_funct_1(u3_abcmiz_0(A))
        & v1_funct_2(u3_abcmiz_0(A),u1_struct_0(A),k5_finsub_1(u1_abcmiz_0(A)))
        & m2_relset_1(u3_abcmiz_0(A),u1_struct_0(A),k5_finsub_1(u1_abcmiz_0(A))) ) ) )).

fof(dt_u4_abcmiz_0,axiom,(
    ! [A] :
      ( l3_abcmiz_0(A)
     => ( v1_funct_1(u4_abcmiz_0(A))
        & v1_funct_2(u4_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A))
        & m2_relset_1(u4_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A)) ) ) )).

fof(dt_g1_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v3_abcmiz_0(g1_abcmiz_0(A,B))
        & l1_abcmiz_0(g1_abcmiz_0(A,B)) ) ) )).

fof(free_g1_abcmiz_0,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m1_relset_1(B,A,A) )
     => ! [C,D] :
          ( g1_abcmiz_0(A,B) = g1_abcmiz_0(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(dt_g2_abcmiz_0,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B)) )
     => ( v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E))
        & l2_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) )).

fof(free_g2_abcmiz_0,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B)) )
     => ! [F,G,H,I,J] :
          ( g2_abcmiz_0(A,B,C,D,E) = g2_abcmiz_0(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).

fof(dt_g3_abcmiz_0,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B))
        & v1_funct_1(F)
        & v1_funct_2(F,B,A)
        & m1_relset_1(F,B,A) )
     => ( v11_abcmiz_0(g3_abcmiz_0(A,B,C,D,E,F))
        & l3_abcmiz_0(g3_abcmiz_0(A,B,C,D,E,F)) ) ) )).

fof(free_g3_abcmiz_0,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,B)
        & m1_relset_1(D,B,B)
        & v1_funct_1(E)
        & v1_funct_2(E,A,k5_finsub_1(B))
        & m1_relset_1(E,A,k5_finsub_1(B))
        & v1_funct_1(F)
        & v1_funct_2(F,B,A)
        & m1_relset_1(F,B,A) )
     => ! [G,H,I,J,K,L] :
          ( g3_abcmiz_0(A,B,C,D,E,F) = g3_abcmiz_0(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) )).

fof(t12_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => k3_abcmiz_0(A,B) = a_2_0_abcmiz_0(A,B) ) ) )).

fof(t15_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_abcmiz_0(A,B) = a_2_1_abcmiz_0(A,B) ) ) )).

fof(t81_abcmiz_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( C = a_2_2_abcmiz_0(A,B)
             => ( r1_yellow_0(A,C)
                & k12_abcmiz_0(A,B) = k1_yellow_0(A,C) ) ) ) ) )).

fof(fraenkel_a_2_0_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l2_abcmiz_0(B)
        & m1_subset_1(C,u1_abcmiz_0(B)) )
     => ( r2_hidden(A,a_2_0_abcmiz_0(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & r2_hidden(C,k2_abcmiz_0(B,D)) ) ) ) )).

fof(fraenkel_a_2_1_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v4_abcmiz_0(B)
        & l2_abcmiz_0(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_1_abcmiz_0(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_abcmiz_0(B))
            & A = D
            & r2_hidden(C,k3_abcmiz_0(B,D)) ) ) ) )).

fof(fraenkel_a_2_2_abcmiz_0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v1_abcmiz_0(B)
        & ~ v4_abcmiz_0(B)
        & v9_abcmiz_0(B)
        & v14_abcmiz_0(B)
        & l3_abcmiz_0(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( r2_hidden(A,a_2_2_abcmiz_0(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ? [E] :
                ( v1_finset_1(E)
                & m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(B)))
                & r6_abcmiz_0(B,D,E)
                & k6_abcmiz_0(B,D,E) = C ) ) ) ) )).
%------------------------------------------------------------------------------