SET007 Axioms: SET007+763.ax


%------------------------------------------------------------------------------
% File     : SET007+763 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Morphisms Into Chains. Part I
% 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    : waybel35 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (   6 unit)
%            Number of atoms       :  547 (  24 equality)
%            Maximal formula depth :   23 (   9 average)
%            Number of connectives :  534 (  57 ~  ;   0  |; 275  &)
%                                         (  13 <=>; 189 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   47 (   1 propositional; 0-3 arity)
%            Number of functors    :   28 (   0 constant; 1-4 arity)
%            Number of variables   :  220 (   0 singleton; 205 !;  15 ?)
%            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(rc1_waybel35,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_realset1(B) ) )).

fof(cc1_waybel35,axiom,(
    ! [A] :
      ( v1_realset1(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_realset1(B) ) ) )).

fof(rc2_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_realset1(B) ) ) )).

fof(rc3_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_realset1(B) ) ) )).

fof(rc4_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) )).

fof(rc5_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) )).

fof(rc6_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_waybel_4(B,A) ) ) )).

fof(rc7_waybel35,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_waybel_4(B,A)
          & v2_waybel_4(B,A) ) ) )).

fof(rc8_waybel35,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v3_waybel_4(B,A) ) ) )).

fof(rc9_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v4_waybel_4(B,A) ) ) )).

fof(cc2_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v1_waybel35(B,A)
           => ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v4_waybel_4(B,A) ) ) ) ) )).

fof(cc3_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v4_waybel_4(B,A) )
           => v1_waybel35(B,A) ) ) ) )).

fof(cc4_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ( v3_waybel_4(B,A)
              & v1_waybel35(B,A) )
           => ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A)
              & v5_waybel_4(B,A)
              & v1_waybel35(B,A) ) ) ) ) )).

fof(cc5_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v5_waybel_4(B,A)
           => ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v4_waybel_4(B,A)
              & v1_waybel35(B,A) ) ) ) ) )).

fof(rc10_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_waybel_4(B,A)
          & v2_waybel_4(B,A)
          & v4_waybel_4(B,A)
          & v1_waybel35(B,A) ) ) )).

fof(fc1_waybel35,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_4(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( v1_relat_1(k1_waybel35(A,B))
        & v1_funct_1(k1_waybel35(A,B))
        & v1_funct_2(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
        & v5_orders_3(k1_waybel35(A,B),A,k2_yellow_1(k4_lattice7(A))) ) ) )).

fof(rc11_waybel35,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ? [C] :
          ( m1_waybel35(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_realset1(C) ) ) )).

fof(fc2_waybel35,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
        & m1_waybel35(C,A,B) )
     => ~ v1_xboole_0(k2_waybel35(A,B,C)) ) )).

fof(cc6_waybel35,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ! [C] :
          ( m1_waybel35(C,A,B)
         => ( v1_realset1(C)
           => v3_waybel35(C,A,B) ) ) ) )).

fof(rc12_waybel35,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ? [C] :
          ( m1_waybel35(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_realset1(C)
          & v3_waybel35(C,A,B) ) ) )).

fof(t1_waybel35,axiom,(
    ! [A] : r1_relat_2(k1_yellow_1(A),A) )).

fof(t2_waybel35,axiom,(
    ! [A] : r8_relat_2(k1_yellow_1(A),A) )).

fof(t3_waybel35,axiom,(
    ! [A] : r4_relat_2(k1_yellow_1(A),A) )).

fof(d1_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v1_waybel35(B,A)
          <=> ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v4_waybel_4(B,A) ) ) ) ) )).

fof(d2_waybel35,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A)))) )
             => ( C = k1_waybel35(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_waybel_0(A,k2_yellow_1(k4_lattice7(A)),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) )).

fof(d3_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( m1_waybel35(C,A,B)
              <=> ! [D,E] :
                    ~ ( r2_hidden(D,C)
                      & r2_hidden(E,C)
                      & ~ r2_hidden(k4_tarski(D,E),B)
                      & D != E
                      & ~ r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) )).

fof(t4_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( v1_realset1(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => m1_waybel35(B,A,C) ) ) ) )).

fof(t5_waybel35,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & r2_orders_2(A,D,E) )
                       => r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) )).

fof(t6_waybel35,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_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)
                      & r2_hidden(k4_tarski(D,C),B) )
                   => C = D ) ) ) ) ) )).

fof(t7_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v4_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => m1_waybel35(k2_struct_0(A,k3_yellow_0(A),B),A,C) ) ) ) )).

fof(t8_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => m1_waybel35(k4_subset_1(u1_struct_0(A),C,k1_struct_0(A,k3_yellow_0(A))),A,B) ) ) ) )).

fof(d4_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( v2_waybel35(C,A,B)
              <=> ! [D] :
                    ( m1_waybel35(D,A,B)
                   => ( r1_lattice7(A,C,D)
                     => C = D ) ) ) ) ) ) )).

fof(d5_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C,D] :
              ( D = k2_waybel35(A,B,C)
            <=> ! [E] :
                  ( r2_hidden(E,D)
                <=> ( m1_waybel35(E,A,B)
                    & r1_tarski(C,E) ) ) ) ) ) )).

fof(t9_waybel35,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( r4_orders_1(k1_yellow_1(k2_waybel35(A,B,C)),k2_waybel35(A,B,C))
                & ? [D] :
                    ( r6_orders_1(k1_yellow_1(k2_waybel35(A,B,C)),D)
                    & r1_tarski(C,D) ) ) ) ) ) )).

fof(t10_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(B))
             => ( ( r1_yellow_0(A,C)
                  & r2_hidden(k1_yellow_0(A,C),B) )
               => ( r1_yellow_0(k5_yellow_0(A,B),C)
                  & k1_yellow_0(A,C) = k1_yellow_0(k5_yellow_0(A,B),C) ) ) ) ) ) )).

fof(t11_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_waybel35(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(C))
                 => ( ( r1_yellow_0(A,D)
                      & v2_waybel35(C,A,B) )
                   => r1_yellow_0(k5_yellow_0(A,C),D) ) ) ) ) ) )).

fof(t12_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_waybel35(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(C))
                 => ( ( r2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))
                      & r1_yellow_0(A,D)
                      & v2_waybel35(C,A,B) )
                   => ( k1_yellow_0(k5_yellow_0(A,C),D) = k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))
                      & ( ~ r2_hidden(k1_yellow_0(A,D),C)
                       => r2_orders_2(A,k1_yellow_0(A,D),k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,k1_yellow_0(A,D)),C))) ) ) ) ) ) ) ) )).

fof(t13_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_waybel35(C,A,B) )
             => ( v2_waybel35(C,A,B)
               => v3_lattice3(k5_yellow_0(A,C)) ) ) ) ) )).

fof(t14_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( v2_waybel35(C,A,B)
               => r2_hidden(k3_yellow_0(A),C) ) ) ) ) )).

fof(t15_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( v2_waybel35(C,A,B)
                      & r4_waybel_1(A,D,C)
                      & r2_hidden(k4_tarski(D,k4_yellow_0(A)),B) )
                   => ( r2_hidden(k4_tarski(k4_yellow_0(A),k4_yellow_0(A)),B)
                      & D = k4_yellow_0(A) ) ) ) ) ) ) )).

fof(d6_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
         => ( r1_waybel35(A,B,C)
          <=> ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] :
                    ( m1_subset_1(E,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & r2_hidden(E,B)
                        & r2_hidden(k4_tarski(D,E),C)
                        & D != E
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( r2_hidden(F,B)
                                & r2_hidden(k4_tarski(D,F),C)
                                & r2_hidden(k4_tarski(F,E),C)
                                & D != F ) ) ) ) ) ) ) ) )).

fof(d7_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( v3_waybel35(C,A,B)
              <=> r1_waybel35(A,C,B) ) ) ) ) )).

fof(t16_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( ( v1_waybel_4(C,A)
            & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_waybel35(A,B,C)
           => ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] :
                    ( m1_subset_1(E,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & r2_hidden(E,B)
                        & r2_hidden(k4_tarski(D,E),C)
                        & D != E
                        & ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( r2_hidden(F,B)
                                & r2_hidden(k4_tarski(D,F),C)
                                & r2_hidden(k4_tarski(F,E),C)
                                & r2_orders_2(A,D,F) ) ) ) ) ) ) ) ) )).

fof(t17_waybel35,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( ( v2_waybel35(C,A,B)
                  & v8_waybel_4(B,A) )
               => r1_waybel35(A,C,B) ) ) ) ) )).

fof(d8_waybel35,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] : k3_waybel35(A,B,C) = k3_xboole_0(k10_relat_1(A,k1_tarski(C)),B) ) )).

fof(t18_waybel35,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C,D] :
          ( r2_hidden(C,k3_waybel35(A,B,D))
        <=> ( r2_hidden(k4_tarski(C,D),A)
            & r2_hidden(C,B) ) ) ) )).

fof(t19_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C,D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => r2_lattice3(A,k4_waybel35(A,B,C,D),D) ) ) ) )).

fof(t20_waybel35,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r1_orders_2(A,D,E)
                       => r1_lattice7(A,k4_waybel35(A,B,C,D),k4_waybel35(A,B,C,E)) ) ) ) ) ) ) )).

fof(t21_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C,D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r2_hidden(D,C)
                  & r2_hidden(k4_tarski(D,D),B)
                  & r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
               => D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) ) ) )).

fof(d9_waybel35,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel35(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(B))
               => ( r1_yellow_0(A,C)
                 => k1_yellow_0(A,C) = k1_yellow_0(k5_yellow_0(A,B),C) ) ) ) ) ) )).

fof(t22_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel35(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_waybel35(C,A,B)
                & m1_waybel35(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & r2_orders_2(A,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_orders_2(A,D,F)
                                  & r2_hidden(k4_tarski(F,E),B)
                                  & F = k1_yellow_0(A,k4_waybel35(A,B,C,F)) ) ) ) ) ) ) ) ) )).

fof(t23_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel35(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & m1_waybel35(C,A,B) )
             => ( ( v4_waybel35(C,A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,C)
                       => r1_yellow_0(A,k4_waybel35(A,B,C,D)) ) )
                  & r1_waybel35(A,C,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                     => D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) ) ) ) ) )).

fof(t24_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                     => ( r1_yellow_0(A,k4_waybel35(A,B,C,D))
                        & D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) )
               => r1_waybel35(A,C,B) ) ) ) ) )).

fof(d10_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C,D] :
              ( D = k5_waybel35(A,B,C)
            <=> ! [E] :
                  ( r2_hidden(E,D)
                <=> E = k1_yellow_0(A,k4_waybel35(A,B,C,E)) ) ) ) ) )).

fof(t25_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_waybel35(C,A,B)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
               => m1_waybel35(k6_waybel35(A,B,C),A,B) ) ) ) ) )).

fof(t26_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_yellow_0(A,k4_waybel35(A,B,C,D)) )
               => v4_waybel35(k6_waybel35(A,B,C),A) ) ) ) ) )).

fof(t28_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel35(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_waybel35(C,A,B)
                & m1_waybel35(C,A,B) )
             => r1_waybel35(A,k6_waybel35(A,B,C),B) ) ) ) )).

fof(t29_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel35(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_waybel35(C,A,B)
                & m1_waybel35(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & r2_hidden(E,C)
                          & r2_orders_2(A,D,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_hidden(F,k6_waybel35(A,B,C))
                                  & r2_orders_2(A,D,F)
                                  & r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ) ) )).

fof(dt_m1_waybel35,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ! [C] :
          ( m1_waybel35(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).

fof(existence_m1_waybel35,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ? [C] : m1_waybel35(C,A,B) ) )).

fof(dt_k1_waybel35,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A)
        & v2_waybel_4(B,A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => ( v1_funct_1(k1_waybel35(A,B))
        & v1_funct_2(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A))))
        & m2_relset_1(k1_waybel35(A,B),u1_struct_0(A),u1_struct_0(k2_yellow_1(k4_lattice7(A)))) ) ) )).

fof(dt_k2_waybel35,axiom,(
    $true )).

fof(dt_k3_waybel35,axiom,(
    $true )).

fof(dt_k4_waybel35,axiom,(
    ! [A,B,C,D] :
      ( ( l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k4_waybel35(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(redefinition_k4_waybel35,axiom,(
    ! [A,B,C,D] :
      ( ( l1_struct_0(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => k4_waybel35(A,B,C,D) = k3_waybel35(B,C,D) ) )).

fof(dt_k5_waybel35,axiom,(
    $true )).

fof(dt_k6_waybel35,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => m1_subset_1(k6_waybel35(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(redefinition_k6_waybel35,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
     => k6_waybel35(A,B,C) = k5_waybel35(A,B,C) ) )).

fof(t27_waybel35,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_waybel35(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v3_waybel35(C,A,B)
                & m1_waybel35(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,k6_waybel35(A,B,C))
                   => D = k1_yellow_0(A,a_4_0_waybel35(A,B,C,D)) ) ) ) ) ) )).

fof(fraenkel_a_4_0_waybel35,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & v1_waybel35(C,B)
        & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
        & v3_waybel35(D,B,C)
        & m1_waybel35(D,B,C)
        & m1_subset_1(E,u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_0_waybel35(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & r2_hidden(F,k6_waybel35(B,C,D))
            & r2_hidden(k4_tarski(F,E),C) ) ) ) )).
%------------------------------------------------------------------------------