SET007 Axioms: SET007+496.ax


%------------------------------------------------------------------------------
% File     : SET007+496 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Irreducible and Prime Elements
% 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    : waybel_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   61 (   0 unit)
%            Number of atoms       :  722 (  31 equality)
%            Maximal formula depth :   20 (  11 average)
%            Number of connectives :  729 (  68 ~  ;   0  |; 458  &)
%                                         (  32 <=>; 171 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   0 propositional; 1-3 arity)
%            Number of functors    :   42 (   7 constant; 0-5 arity)
%            Number of variables   :  179 (   0 singleton; 168 !;  11 ?)
%            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_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_orders_2(B,A)
           => ( v5_orders_2(B,A)
              & v1_waybel_0(B,A)
              & v2_waybel_0(B,A) ) ) ) ) )).

fof(rc1_waybel_6,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v2_waybel_1(A)
      & v2_waybel_3(A)
      & v3_waybel_3(A) ) )).

fof(rc2_waybel_6,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v18_waybel_0(C,A,B)
          & v20_waybel_0(C,A,B)
          & v22_waybel_0(C,A,B) ) ) )).

fof(rc3_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v2_waybel_0(B,A)
          & v13_waybel_0(B,A)
          & v1_waybel_6(B,A) ) ) )).

fof(rc4_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(A))
          & v2_waybel_6(B,A) ) ) )).

fof(rc5_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_subset_1(B,u1_struct_0(A))
          & v5_waybel_6(B,A) ) ) )).

fof(t1_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v19_waybel_0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k7_yellow_2(u1_struct_0(A),B,C,k12_lattice3(A,D,E)) = k12_lattice3(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) )).

fof(t2_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v20_waybel_0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k7_yellow_2(u1_struct_0(A),B,C,k13_lattice3(A,D,E)) = k13_lattice3(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) )).

fof(t3_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v2_waybel_1(B)
                  & v19_waybel_0(C,A,B)
                  & v20_waybel_0(C,A,B)
                  & v2_funct_1(C) )
               => v2_waybel_1(A) ) ) ) ) )).

fof(t4_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v18_waybel_0(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( ( v2_waybel_2(B)
                  & v19_waybel_0(C,A,B)
                  & v2_funct_1(C) )
               => v2_waybel_2(A) ) ) ) ) )).

fof(d1_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel_6(B,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)
                            & r1_waybel_3(A,D,C) ) ) ) ) ) ) ) )).

fof(t5_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ~ ( r2_hidden(C,B)
                    & r1_xboole_0(k1_waybel_3(A,C),B) ) ) ) ) ) )).

fof(t7_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => v1_waybel_6(k2_waybel_3(A,B),A) ) ) )).

fof(t8_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r1_waybel_3(A,B,C)
                  & ! [D] :
                      ( ( ~ v1_xboole_0(D)
                        & v2_waybel_0(D,A)
                        & v13_waybel_0(D,A)
                        & v1_waybel_6(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => ~ ( r2_hidden(C,D)
                          & r1_tarski(D,k2_waybel_3(A,B)) ) ) ) ) ) ) )).

fof(t9_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & v1_waybel_6(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B))
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r3_orders_2(A,C,D)
                          & r3_waybel_4(A,k3_subset_1(u1_struct_0(A),B),D) ) ) ) ) ) ) )).

fof(d2_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v2_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( B = k11_lattice3(A,C,D)
                        & C != B
                        & D != B ) ) ) ) ) ) )).

fof(d3_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( B = k10_lattice3(A,C,D)
                        & C != B
                        & D != B ) ) ) ) ) ) )).

fof(d4_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = k3_waybel_6(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                <=> v2_waybel_6(C,A) ) ) ) ) ) )).

fof(t10_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v2_waybel_6(k4_yellow_0(A),A) ) )).

fof(t11_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v2_waybel_6(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( B = k2_yellow_0(A,C)
                 => r2_hidden(B,C) ) ) ) ) ) )).

fof(t12_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v1_xboole_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)))
              & v2_waybel_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),A)
              & v13_waybel_0(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),A)
              & m1_subset_1(k6_subset_1(u1_struct_0(A),k7_waybel_0(A,B),k1_struct_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) )
           => v2_waybel_6(B,A) ) ) ) )).

fof(t13_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v2_waybel_0(C,A)
                & v13_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r3_waybel_4(A,k3_subset_1(u1_struct_0(A),C),B)
               => v2_waybel_6(B,A) ) ) ) ) )).

fof(t14_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( ~ r3_orders_2(A,C,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( v2_waybel_6(D,A)
                          & r3_orders_2(A,B,D)
                          & ~ r3_orders_2(A,C,D) ) ) ) ) ) ) )).

fof(d5_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,C),B))
                  & C = k2_yellow_0(A,k5_subset_1(u1_struct_0(A),k7_waybel_0(A,C),B)) ) ) ) ) ) )).

fof(t15_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] :
                    ( m1_subset_1(D,k1_zfmisc_1(B))
                    & C = k2_yellow_0(A,D) ) ) ) ) ) )).

fof(t16_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( r1_tarski(B,C)
                    & ! [D] :
                        ( m1_subset_1(D,k1_zfmisc_1(C))
                       => r2_hidden(k2_yellow_0(A,D),C) ) )
                 => u1_struct_0(A) = C ) ) ) ) ) )).

fof(t17_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( ~ r3_orders_2(A,D,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r3_orders_2(A,C,E)
                                & ~ r3_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).

fof(t18_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = k6_subset_1(u1_struct_0(A),k3_waybel_6(A),k1_struct_0(A,k4_yellow_0(A)))
           => v4_waybel_6(B,A) ) ) ) )).

fof(t19_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v4_waybel_6(B,A)
                  & r1_tarski(B,C) )
               => v4_waybel_6(C,A) ) ) ) ) )).

fof(d6_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_waybel_6(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r1_orders_2(A,k11_lattice3(A,C,D),B)
                        & ~ r1_orders_2(A,C,B)
                        & ~ r1_orders_2(A,D,B) ) ) ) ) ) ) )).

fof(d7_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( B = k4_waybel_6(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r2_hidden(C,B)
                <=> v5_waybel_6(C,A) ) ) ) ) ) )).

fof(d8_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v6_waybel_6(B,A)
          <=> v5_waybel_6(k8_lattice3(A,B),k7_lattice3(A)) ) ) ) )).

fof(t20_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => v5_waybel_6(k4_yellow_0(A),A) ) )).

fof(t21_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => v6_waybel_6(k3_yellow_0(A),A) ) )).

fof(t22_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_waybel_6(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ~ ( r1_orders_2(A,k2_yellow_0(A,C),B)
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( r2_hidden(D,C)
                            & r1_orders_2(A,D,B) ) ) ) ) ) ) ) )).

fof(t23_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v6_waybel_6(B,A)
          <=> ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ~ ( r3_orders_2(A,B,k1_yellow_0(A,C))
                    & ! [D] :
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ~ ( r2_hidden(D,C)
                            & r3_orders_2(A,B,D) ) ) ) ) ) ) ) )).

fof(t24_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_waybel_6(B,A)
           => v2_waybel_6(B,A) ) ) ) )).

fof(t25_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_waybel_6(B,A)
          <=> ! [C,D] :
                ( ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(C))))
                  & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(C)))) )
               => ( ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k7_yellow_2(u1_struct_0(A),k3_yellow_1(k1_tarski(C)),D,E) = k1_xboole_0
                      <=> r3_orders_2(A,E,B) ) )
                 => ( v19_waybel_0(D,A,k3_yellow_1(k1_tarski(C)))
                    & v20_waybel_0(D,A,k3_yellow_1(k1_tarski(C))) ) ) ) ) ) ) )).

fof(t26_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k4_yellow_0(A)
           => ( v5_waybel_6(B,A)
            <=> ( ~ v1_xboole_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)))
                & v2_waybel_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
                & v13_waybel_0(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A)
                & m1_subset_1(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).

fof(t27_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v5_waybel_6(B,A)
          <=> v2_waybel_6(B,A) ) ) ) )).

fof(t28_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => k4_waybel_6(A) = k3_waybel_6(A) ) )).

fof(t29_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k4_yellow_0(A)
           => ( v5_waybel_6(B,A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r2_orders_2(A,B,C)
                   => C = k4_yellow_0(A) ) ) ) ) ) ) )).

fof(t30_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_1(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k4_yellow_0(A)
           => ( v5_waybel_6(B,A)
            <=> ? [C] :
                  ( ~ v1_xboole_0(C)
                  & v2_waybel_0(C,A)
                  & v13_waybel_0(C,A)
                  & v1_waybel_6(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                  & r3_waybel_4(A,k3_subset_1(u1_struct_0(A),C),B) ) ) ) ) ) )).

fof(t31_waybel_6,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_funct_1(k5_funct_3(B,u1_struct_0(A)))
            & v1_funct_2(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0))))
            & m2_relset_1(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0)))) ) ) ) )).

fof(t32_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k8_funct_2(u1_struct_0(A),k2_tarski(np__0,np__1),k5_funct_3(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),u1_struct_0(A)),C) = k1_xboole_0
              <=> r1_orders_2(A,C,B) ) ) ) ) )).

fof(t33_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(k1_tarski(k1_xboole_0)))) )
         => ! [C] :
              ( ( v5_waybel_6(C,A)
                & m1_subset_1(C,u1_struct_0(A)) )
             => ( k5_funct_3(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,C)),u1_struct_0(A)) = B
               => ( v19_waybel_0(B,A,k3_yellow_1(k1_tarski(k1_xboole_0)))
                  & v20_waybel_0(B,A,k3_yellow_1(k1_tarski(k1_xboole_0))) ) ) ) ) ) )).

fof(t34_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v4_waybel_6(k4_waybel_6(A),A)
       => ( v2_waybel_1(A)
          & v2_waybel_2(A) ) ) ) )).

fof(t35_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(A)
      <=> v4_waybel_6(k4_waybel_6(A),A) ) ) )).

fof(t36_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(A)
      <=> v9_waybel_1(A) ) ) )).

fof(t37_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & B = k1_yellow_0(A,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                     => v6_waybel_6(D,A) ) ) ) )
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,k3_xboole_0(k1_waybel_3(A,B),k4_waybel_6(k7_lattice3(A)))) ) ) ) )).

fof(t38_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_waybel_5(A)
      <=> ( v3_waybel_3(A)
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] :
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                  & B = k1_yellow_0(A,C)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(D,C)
                       => v6_waybel_6(D,A) ) ) ) ) ) ) ) )).

fof(t39_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_waybel_5(A)
      <=> ( v2_waybel_1(A)
          & v3_waybel_3(A)
          & v3_waybel_3(k7_lattice3(A)) ) ) ) )).

fof(s1_waybel_6,axiom,
    ( ! [A] :
        ( m1_subset_1(A,u1_struct_0(f1_s1_waybel_6))
       => ~ ( r2_hidden(A,f2_s1_waybel_6)
            & ! [B] :
                ( m1_subset_1(B,u1_struct_0(f1_s1_waybel_6))
               => ~ ( r2_hidden(B,f3_s1_waybel_6)
                    & p1_s1_waybel_6(A,B) ) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f2_s1_waybel_6,f3_s1_waybel_6)
        & m2_relset_1(A,f2_s1_waybel_6,f3_s1_waybel_6)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s1_waybel_6))
           => ~ ( r2_hidden(B,f2_s1_waybel_6)
                & ! [C] :
                    ( m1_subset_1(C,u1_struct_0(f1_s1_waybel_6))
                   => ~ ( r2_hidden(C,f3_s1_waybel_6)
                        & C = k1_funct_1(A,B)
                        & p1_s1_waybel_6(B,C) ) ) ) ) ) )).

fof(dt_k1_waybel_6,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,B,B)
        & m1_relset_1(C,B,B)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_funct_1(k1_waybel_6(A,B,C,D))
        & v1_funct_2(k1_waybel_6(A,B,C,D),B,B)
        & m2_relset_1(k1_waybel_6(A,B,C,D),B,B) ) ) )).

fof(redefinition_k1_waybel_6,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,B,B)
        & m1_relset_1(C,B,B)
        & m1_subset_1(D,k5_numbers) )
     => k1_waybel_6(A,B,C,D) = k9_funct_7(C,D) ) )).

fof(dt_k2_waybel_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(D)
        & v1_funct_2(D,B,C)
        & m1_relset_1(D,B,C)
        & m1_subset_1(E,B) )
     => m1_subset_1(k2_waybel_6(A,B,C,D,E),u1_struct_0(A)) ) )).

fof(redefinition_k2_waybel_6,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(D)
        & v1_funct_2(D,B,C)
        & m1_relset_1(D,B,C)
        & m1_subset_1(E,B) )
     => k2_waybel_6(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k3_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m1_subset_1(k3_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k4_waybel_6,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m1_subset_1(k4_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(t6_waybel_6,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_6(B,A)
          <=> B = k3_tarski(a_2_0_waybel_6(A,B)) ) ) ) )).

fof(fraenkel_a_2_0_waybel_6,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v24_waybel_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v13_waybel_0(C,B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_waybel_6(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k2_waybel_3(B,D)
            & r2_hidden(D,C) ) ) ) )).
%------------------------------------------------------------------------------