SET007 Axioms: SET007+663.ax


%------------------------------------------------------------------------------
% File     : SET007+663 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The J'onsson Theorem about the Representation of Modular Lattices
% 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    : lattice8 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   71 (   8 unit)
%            Number of atoms       : 1003 (  67 equality)
%            Maximal formula depth :   34 (  13 average)
%            Number of connectives : 1014 (  82 ~  ;   5  |; 663  &)
%                                         (  12 <=>; 252 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   59 (   1 propositional; 0-6 arity)
%            Number of functors    :   57 (   6 constant; 0-5 arity)
%            Number of variables   :  282 (   0 singleton; 265 !;  17 ?)
%            Maximal term depth    :    6 (   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_lattice8,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(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)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow11(A)
      & v2_waybel_1(A)
      & v6_group_1(A) ) )).

fof(rc2_lattice8,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ? [B] :
          ( m1_yellow_0(B,k1_lattice5(A))
          & ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v4_yellow_0(B,k1_lattice5(A))
          & v5_yellow_0(B,k1_lattice5(A))
          & v6_yellow_0(B,k1_lattice5(A))
          & v1_lattice3(B)
          & v2_lattice3(B)
          & ~ v3_realset2(B)
          & v1_lattice8(B) ) ) )).

fof(fc1_lattice8,axiom,(
    ! [A] : ~ v1_xboole_0(k1_lattice8(A)) )).

fof(fc2_lattice8,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v3_ordinal1(B) )
     => ~ v1_xboole_0(k3_lattice8(A,B)) ) )).

fof(fc3_lattice8,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ~ v1_xboole_0(k7_lattice8(A,B,C)) ) )).

fof(d1_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( r1_lattice8(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ( r2_hidden(k1_domain_1(A,A,D,E),B)
                         => r2_hidden(k1_domain_1(A,A,D,E),C) ) ) ) ) ) ) ) )).

fof(d2_lattice8,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_lattice8(A)
      <=> ? [B] :
            ( ~ v1_xboole_0(B)
            & ! [C] :
                ( r2_hidden(C,u1_struct_0(A))
               => ( v1_partfun1(C,B,B)
                  & v3_relat_2(C)
                  & v8_relat_2(C)
                  & m2_relset_1(C,B,B) ) )
            & ? [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & ! [D] :
                    ( ( v1_partfun1(D,B,B)
                      & v3_relat_2(D)
                      & v8_relat_2(D)
                      & m2_relset_1(D,B,B) )
                   => ! [E] :
                        ( ( v1_partfun1(E,B,B)
                          & v3_relat_2(E)
                          & v8_relat_2(E)
                          & m2_relset_1(E,B,B) )
                       => ! [F,G] :
                            ~ ( r2_hidden(D,u1_struct_0(A))
                              & r2_hidden(E,u1_struct_0(A))
                              & r2_hidden(k4_tarski(F,G),k5_eqrel_1(B,D,E))
                              & ! [H] :
                                  ( ( ~ v1_xboole_0(H)
                                    & m2_finseq_1(H,B) )
                                 => ~ ( k3_finseq_1(H) = C
                                      & r1_lattice5(B,H,F,G,D,E) ) ) ) ) ) ) ) ) ) )).

fof(d3_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_lattice8(A,B)
          <=> ? [C] :
                ( ~ v1_realset1(C)
                & ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
                    & v19_waybel_0(D,A,k1_lattice5(C))
                    & v20_waybel_0(D,A,k1_lattice5(C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
                    & v2_funct_1(D)
                    & v1_lattice8(k2_lattice5(A,k1_lattice5(C),D))
                    & ? [E] :
                        ( v1_partfun1(E,C,C)
                        & v3_relat_2(E)
                        & v8_relat_2(E)
                        & m2_relset_1(E,C,C)
                        & r2_hidden(E,u1_struct_0(k2_lattice5(A,k1_lattice5(C),D)))
                        & E != k6_partfun1(C) )
                    & r1_xreal_0(k3_lattice5(C,k2_lattice5(A,k1_lattice5(C),D)),B) ) ) ) ) ) )).

fof(t1_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => r1_ordinal1(k1_ordinal1(k1_xboole_0),k8_lattice5(A,B,C)) ) ) ) )).

fof(t2_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v3_realset2(A)
        & l1_orders_2(A) )
     => v1_yellow11(A) ) )).

fof(t3_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v5_yellow_0(B,k1_lattice5(A))
            & v6_yellow_0(B,k1_lattice5(A))
            & m1_yellow_0(B,k1_lattice5(A)) )
         => ~ ( ~ v3_realset2(B)
              & ! [C] :
                  ( ( v1_partfun1(C,A,A)
                    & v3_relat_2(C)
                    & v8_relat_2(C)
                    & m2_relset_1(C,A,A) )
                 => ~ ( r2_hidden(C,u1_struct_0(B))
                      & C != k6_partfun1(A) ) ) ) ) ) )).

fof(t4_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(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_yellow_0(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)) )
             => ( ( v17_waybel_0(C,A,B)
                  & v18_waybel_0(C,A,B) )
               => ( v19_waybel_0(C,A,B)
                  & v20_waybel_0(C,A,B) ) ) ) ) ) )).

fof(t5_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(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_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v1_yellow11(A) )
           => v1_yellow11(B) ) ) ) )).

fof(t6_lattice8,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] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v5_orders_3(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => v1_yellow_0(k2_yellow_2(A,B,C)) ) ) ) )).

fof(t7_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(D)))
                        & v19_waybel_0(E,A,k1_lattice5(D))
                        & v20_waybel_0(E,A,k1_lattice5(D))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_lattice5(D))) )
                     => ( ( v2_funct_1(E)
                          & r3_orders_2(k2_yellow_2(A,k1_lattice5(D),E),k1_waybel_0(A,k2_yellow_2(A,k1_lattice5(D),E),k2_waybel_1(A,k1_lattice5(D),E),B),k1_waybel_0(A,k2_yellow_2(A,k1_lattice5(D),E),k2_waybel_1(A,k1_lattice5(D),E),C)) )
                       => r3_orders_2(A,B,C) ) ) ) ) ) ) )).

fof(t8_lattice8,axiom,(
    ! [A] :
      ( ~ v1_realset1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,k1_lattice5(A))
            & v5_yellow_0(B,k1_lattice5(A))
            & v6_yellow_0(B,k1_lattice5(A))
            & v1_lattice8(B)
            & m1_yellow_0(B,k1_lattice5(A)) )
         => ! [C] :
              ( ( v1_partfun1(C,A,A)
                & v3_relat_2(C)
                & v8_relat_2(C)
                & m2_relset_1(C,A,A) )
             => ( ( r2_hidden(C,u1_struct_0(B))
                  & r1_xreal_0(k3_lattice5(A,B),np__2) )
               => ( C = k6_partfun1(A)
                  | v1_yellow11(B) ) ) ) ) ) )).

fof(t9_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( r2_lattice8(A,np__2)
       => v1_yellow11(A) ) ) )).

fof(d4_lattice8,axiom,(
    ! [A] : k1_lattice8(A) = k2_xboole_0(A,k2_tarski(k1_tarski(A),k1_tarski(k1_tarski(A)))) )).

fof(d5_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B))
                        & m2_relset_1(E,k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B)) )
                     => ( E = k2_lattice8(A,B,C,D)
                      <=> ( ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => k1_binop_1(E,F,G) = k4_lattice5(A,B,C,F,G) ) )
                          & k1_binop_1(E,k1_tarski(A),k1_tarski(A)) = k3_yellow_0(B)
                          & k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(A))) = k3_yellow_0(B)
                          & k1_binop_1(E,k1_tarski(A),k1_tarski(k1_tarski(A))) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                          & k1_binop_1(E,k1_tarski(k1_tarski(A)),k1_tarski(A)) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                          & ! [F] :
                              ( m1_subset_1(F,A)
                             => ( k1_binop_1(E,F,k1_tarski(A)) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,k1_tarski(A),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,F,k1_tarski(k1_tarski(A))) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D))
                                & k1_binop_1(E,k1_tarski(k1_tarski(A)),F) = k13_lattice3(B,k4_lattice5(A,B,C,F,k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)) ) ) ) ) ) ) ) ) ) )).

fof(t10_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v2_lattice5(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                   => v2_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) )).

fof(t11_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v1_lattice5(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                   => v1_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) )).

fof(t12_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( v1_yellow11(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                  & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
               => ( ( v1_lattice5(C,A,B)
                    & v3_lattice5(C,A,B) )
                 => ! [D] :
                      ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                     => ( r3_orders_2(B,k4_lattice5(A,B,C,k8_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k9_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)),k13_lattice3(B,k10_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D),k11_mcart_1(A,A,u1_struct_0(B),u1_struct_0(B),D)))
                       => v3_lattice5(k2_lattice8(A,B,C,D),k1_lattice8(A),B) ) ) ) ) ) ) ) )).

fof(t13_lattice8,axiom,(
    ! [A] : r1_tarski(A,k1_lattice8(A)) )).

fof(t14_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B)))
                 => r1_tarski(C,k2_lattice8(A,B,C,D)) ) ) ) ) )).

fof(d6_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => ! [C] :
              ( C = k3_lattice8(A,B)
            <=> ? [D] :
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & v5_ordinal1(D)
                  & C = k1_ordinal2(D)
                  & k1_relat_1(D) = k1_ordinal1(B)
                  & k1_funct_1(D,k1_xboole_0) = A
                  & ! [E] :
                      ( v3_ordinal1(E)
                     => ( r2_hidden(k1_ordinal1(E),k1_ordinal1(B))
                       => k1_funct_1(D,k1_ordinal1(E)) = k1_lattice8(k1_funct_1(D,E)) ) )
                  & ! [E] :
                      ( v3_ordinal1(E)
                     => ( ( r2_hidden(E,k1_ordinal1(B))
                          & v4_ordinal1(E) )
                       => ( E = k1_xboole_0
                          | k1_funct_1(D,E) = k3_tarski(k2_relat_1(k2_ordinal1(D,E))) ) ) ) ) ) ) ) )).

fof(t15_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k3_lattice8(A,k1_xboole_0) = A ) )).

fof(t16_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => k3_lattice8(A,k1_ordinal1(B)) = k1_lattice8(k3_lattice8(A,B)) ) ) )).

fof(t17_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v5_ordinal1(C) )
             => ( ( v4_ordinal1(B)
                  & k1_relat_1(C) = B
                  & ! [D] :
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,B)
                       => k1_funct_1(C,D) = k3_lattice8(A,D) ) ) )
               => ( B = k1_xboole_0
                  | k3_lattice8(A,B) = k3_tarski(k2_relat_1(C)) ) ) ) ) ) )).

fof(t18_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => r1_tarski(A,k3_lattice8(A,B)) ) ) )).

fof(d7_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => ( r2_hidden(E,k1_relat_1(D))
                       => k4_lattice8(A,B,C,D,E) = k1_funct_1(D,E) ) ) ) ) ) ) )).

fof(d8_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => ! [F] :
                          ( F = k5_lattice8(A,B,C,D,E)
                        <=> ? [G] :
                              ( v1_relat_1(G)
                              & v1_funct_1(G)
                              & v5_ordinal1(G)
                              & F = k1_ordinal2(G)
                              & k1_relat_1(G) = k1_ordinal1(E)
                              & k1_funct_1(G,k1_xboole_0) = C
                              & ! [H] :
                                  ( v3_ordinal1(H)
                                 => ( r2_hidden(k1_ordinal1(H),k1_ordinal1(E))
                                   => k1_funct_1(G,k1_ordinal1(H)) = k2_lattice8(k3_lattice8(A,H),B,k11_lattice5(k3_lattice8(A,H),B,k1_funct_1(G,H)),k4_lattice8(A,B,C,D,H)) ) )
                              & ! [H] :
                                  ( v3_ordinal1(H)
                                 => ( ( r2_hidden(H,k1_ordinal1(E))
                                      & v4_ordinal1(H) )
                                   => ( H = k1_xboole_0
                                      | k1_funct_1(G,H) = k3_tarski(k2_relat_1(k2_ordinal1(G,H))) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => k5_lattice8(A,B,C,D,k1_xboole_0) = C ) ) ) ) )).

fof(t20_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => k5_lattice8(A,B,C,D,k1_ordinal1(E)) = k2_lattice8(k3_lattice8(A,E),B,k11_lattice5(k3_lattice8(A,E),B,k5_lattice8(A,B,C,D,E)),k4_lattice8(A,B,C,D,E)) ) ) ) ) ) )).

fof(t21_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v5_ordinal1(E) )
                     => ! [F] :
                          ( v3_ordinal1(F)
                         => ( ( v4_ordinal1(F)
                              & k1_relat_1(E) = F
                              & ! [G] :
                                  ( v3_ordinal1(G)
                                 => ( r2_hidden(G,F)
                                   => k1_funct_1(E,G) = k5_lattice8(A,B,C,D,G) ) ) )
                           => ( F = k1_xboole_0
                              | k5_lattice8(A,B,C,D,F) = k3_tarski(k2_relat_1(E)) ) ) ) ) ) ) ) ) )).

fof(t22_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( v3_ordinal1(B)
         => ! [C] :
              ( v3_ordinal1(C)
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ( r1_ordinal1(C,D)
                   => r1_tarski(k3_lattice8(A,C),k3_lattice8(A,D)) ) ) ) ) ) )).

fof(t23_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => ( v1_funct_1(k5_lattice8(A,B,C,D,E))
                        & v1_funct_2(k5_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B))
                        & m2_relset_1(k5_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B)) ) ) ) ) ) ) )).

fof(t24_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => r1_tarski(C,k6_lattice8(A,B,C,D,E)) ) ) ) ) ) )).

fof(t25_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( v3_ordinal1(E)
                     => ! [F] :
                          ( m1_lattice5(F,A,B,C)
                         => ( r1_ordinal1(D,E)
                           => r1_tarski(k6_lattice8(A,B,C,F,D),k6_lattice8(A,B,C,F,E)) ) ) ) ) ) ) ) )).

fof(t26_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v2_lattice5(C,A,B)
               => ! [D] :
                    ( m1_lattice5(D,A,B,C)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => v2_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) )).

fof(t27_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( v1_lattice5(C,A,B)
               => ! [D] :
                    ( m1_lattice5(D,A,B,C)
                   => ! [E] :
                        ( v3_ordinal1(E)
                       => v1_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) )).

fof(t28_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ( v1_yellow11(B)
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                  & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
               => ( ( v1_lattice5(C,A,B)
                    & v3_lattice5(C,A,B) )
                 => ! [D] :
                      ( v3_ordinal1(D)
                     => ! [E] :
                          ( m1_lattice5(E,A,B,C)
                         => ( r1_ordinal1(D,k8_lattice5(A,B,C))
                           => v3_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B) ) ) ) ) ) ) ) ) )).

fof(t29_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v1_yellow11(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( v3_ordinal1(D)
                 => ! [E] :
                      ( m1_lattice5(E,A,B,C)
                     => ( r1_ordinal1(D,k8_lattice5(A,B,C))
                       => ( v1_funct_1(k6_lattice8(A,B,C,E,D))
                          & v1_funct_2(k6_lattice8(A,B,C,E,D),k2_zfmisc_1(k3_lattice8(A,D),k3_lattice8(A,D)),u1_struct_0(B))
                          & v1_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
                          & v2_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
                          & v3_lattice5(k6_lattice8(A,B,C,E,D),k3_lattice8(A,D),B)
                          & m2_relset_1(k6_lattice8(A,B,C,E,D),k2_zfmisc_1(k3_lattice8(A,D),k3_lattice8(A,D)),u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(d9_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => k7_lattice8(A,B,C) = k3_lattice8(A,k8_lattice5(A,B,C)) ) ) ) )).

fof(d10_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice5(D,A,B,C)
                 => k8_lattice8(A,B,C,D) = k6_lattice8(A,B,C,D,k8_lattice5(A,B,C)) ) ) ) ) )).

fof(d11_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(D,D),u1_struct_0(B))
                        & v1_lattice5(E,D,B)
                        & v2_lattice5(E,D,B)
                        & v3_lattice5(E,D,B)
                        & m2_relset_1(E,k2_zfmisc_1(D,D),u1_struct_0(B)) )
                     => ( r3_lattice8(A,B,C,D,E)
                      <=> ? [F] :
                            ( m1_lattice5(F,A,B,C)
                            & D = k7_lattice8(A,B,C)
                            & E = k8_lattice8(A,B,C,F) ) ) ) ) ) ) ) )).

fof(t30_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(D,D),u1_struct_0(B))
                        & v1_lattice5(E,D,B)
                        & v2_lattice5(E,D,B)
                        & v3_lattice5(E,D,B)
                        & m2_relset_1(E,k2_zfmisc_1(D,D),u1_struct_0(B)) )
                     => ( r3_lattice8(A,B,C,D,E)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(B))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(B))
                                       => ~ ( r3_orders_2(B,k4_lattice5(A,B,C,F,G),k13_lattice3(B,H,I))
                                            & ! [J] :
                                                ( m1_subset_1(J,D)
                                               => ! [K] :
                                                    ( m1_subset_1(K,D)
                                                   => ~ ( k1_binop_1(E,F,J) = H
                                                        & k4_lattice5(D,B,E,J,K) = k12_lattice3(B,k13_lattice3(B,k4_lattice5(A,B,C,F,G),H),I)
                                                        & k1_binop_1(E,K,G) = H ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d12_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v1_yellow11(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( m1_lattice8(D,A,B,C)
                  <=> ( k1_relat_1(D) = k5_numbers
                      & k1_funct_1(D,np__0) = k4_tarski(A,C)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ? [F] :
                              ( ~ v1_xboole_0(F)
                              & ? [G] :
                                  ( v1_funct_1(G)
                                  & v1_funct_2(G,k2_zfmisc_1(F,F),u1_struct_0(B))
                                  & v1_lattice5(G,F,B)
                                  & v2_lattice5(G,F,B)
                                  & v3_lattice5(G,F,B)
                                  & m2_relset_1(G,k2_zfmisc_1(F,F),u1_struct_0(B))
                                  & ? [H] :
                                      ( ~ v1_xboole_0(H)
                                      & ? [I] :
                                          ( v1_funct_1(I)
                                          & v1_funct_2(I,k2_zfmisc_1(H,H),u1_struct_0(B))
                                          & v1_lattice5(I,H,B)
                                          & v2_lattice5(I,H,B)
                                          & v3_lattice5(I,H,B)
                                          & m2_relset_1(I,k2_zfmisc_1(H,H),u1_struct_0(B))
                                          & r3_lattice8(F,B,G,H,I)
                                          & k1_funct_1(D,E) = k4_tarski(F,G)
                                          & k1_funct_1(D,k1_nat_1(E,np__1)) = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t31_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v1_yellow11(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice8(D,A,B,C)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(E,F)
                           => r1_tarski(k1_mcart_1(k1_funct_1(D,E)),k1_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) )).

fof(t32_lattice8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_yellow_0(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v1_yellow11(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & v1_lattice5(C,A,B)
                & v2_lattice5(C,A,B)
                & v3_lattice5(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ! [D] :
                  ( m1_lattice8(D,A,B,C)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(E,F)
                           => r1_tarski(k2_mcart_1(k1_funct_1(D,E)),k2_mcart_1(k1_funct_1(D,F))) ) ) ) ) ) ) ) )).

fof(t36_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow11(A)
        & l1_orders_2(A) )
     => r2_lattice8(A,np__2) ) )).

fof(t37_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( r2_lattice8(A,np__2)
      <=> v1_yellow11(A) ) ) )).

fof(dt_m1_lattice8,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ! [D] :
          ( m1_lattice8(D,A,B,C)
         => ( v1_relat_1(D)
            & v1_funct_1(D) ) ) ) )).

fof(existence_m1_lattice8,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ? [D] : m1_lattice8(D,A,B,C) ) )).

fof(reflexivity_r1_lattice8,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A)
        & m1_relset_1(C,A,A) )
     => r1_lattice8(A,B,B) ) )).

fof(redefinition_r1_lattice8,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A)
        & m1_relset_1(C,A,A) )
     => ( r1_lattice8(A,B,C)
      <=> r1_tarski(B,C) ) ) )).

fof(dt_k1_lattice8,axiom,(
    $true )).

fof(dt_k2_lattice8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) )
     => ( v1_funct_1(k2_lattice8(A,B,C,D))
        & v1_funct_2(k2_lattice8(A,B,C,D),k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B))
        & m2_relset_1(k2_lattice8(A,B,C,D),k2_zfmisc_1(k1_lattice8(A),k1_lattice8(A)),u1_struct_0(B)) ) ) )).

fof(dt_k3_lattice8,axiom,(
    $true )).

fof(dt_k4_lattice8,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_lattice5(D,A,B,C)
        & v3_ordinal1(E) )
     => m1_subset_1(k4_lattice8(A,B,C,D,E),k4_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E),u1_struct_0(B),u1_struct_0(B))) ) )).

fof(dt_k5_lattice8,axiom,(
    $true )).

fof(dt_k6_lattice8,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_lattice5(D,A,B,C)
        & v3_ordinal1(E) )
     => ( v1_funct_1(k6_lattice8(A,B,C,D,E))
        & v1_funct_2(k6_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B))
        & m2_relset_1(k6_lattice8(A,B,C,D,E),k2_zfmisc_1(k3_lattice8(A,E),k3_lattice8(A,E)),u1_struct_0(B)) ) ) )).

fof(redefinition_k6_lattice8,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_lattice5(D,A,B,C)
        & v3_ordinal1(E) )
     => k6_lattice8(A,B,C,D,E) = k5_lattice8(A,B,C,D,E) ) )).

fof(dt_k7_lattice8,axiom,(
    $true )).

fof(dt_k8_lattice8,axiom,(
    $true )).

fof(dt_k9_lattice8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_lattice5(D,A,B,C) )
     => ( v1_funct_1(k9_lattice8(A,B,C,D))
        & v1_funct_2(k9_lattice8(A,B,C,D),k2_zfmisc_1(k7_lattice8(A,B,C),k7_lattice8(A,B,C)),u1_struct_0(B))
        & v1_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
        & v2_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
        & v3_lattice5(k9_lattice8(A,B,C,D),k7_lattice8(A,B,C),B)
        & m2_relset_1(k9_lattice8(A,B,C,D),k2_zfmisc_1(k7_lattice8(A,B,C),k7_lattice8(A,B,C)),u1_struct_0(B)) ) ) )).

fof(redefinition_k9_lattice8,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & v1_lattice5(C,A,B)
        & v2_lattice5(C,A,B)
        & v3_lattice5(C,A,B)
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_lattice5(D,A,B,C) )
     => k9_lattice8(A,B,C,D) = k8_lattice8(A,B,C,D) ) )).

fof(t33_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow11(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ( C = k3_tarski(a_2_0_lattice8(A,B))
               => ( v1_funct_1(k3_tarski(a_2_1_lattice8(A,B)))
                  & v1_funct_2(k3_tarski(a_2_1_lattice8(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A))
                  & v1_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
                  & v2_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
                  & v3_lattice5(k3_tarski(a_2_1_lattice8(A,B)),C,A)
                  & m2_relset_1(k3_tarski(a_2_1_lattice8(A,B)),k2_zfmisc_1(C,C),u1_struct_0(A)) ) ) ) ) ) )).

fof(t34_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow11(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A))
                    & v1_lattice5(D,C,A)
                    & v2_lattice5(D,C,A)
                    & v3_lattice5(D,C,A)
                    & m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ! [F] :
                          ( m1_subset_1(F,C)
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ~ ( C = k3_tarski(a_2_0_lattice8(A,B))
                                      & D = k3_tarski(a_2_1_lattice8(A,B))
                                      & r3_orders_2(A,k4_lattice5(C,A,D,E,F),k13_lattice3(A,G,H))
                                      & ! [I] :
                                          ( m1_subset_1(I,C)
                                         => ! [J] :
                                              ( m1_subset_1(J,C)
                                             => ~ ( k4_lattice5(C,A,D,E,I) = G
                                                  & k4_lattice5(C,A,D,I,J) = k12_lattice3(A,k13_lattice3(A,k4_lattice5(C,A,D,E,F),G),H)
                                                  & k4_lattice5(C,A,D,J,F) = G ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_lattice8,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow11(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_lattice8(B,u1_struct_0(A),A,k17_lattice5(A))
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A))
                    & v1_lattice5(D,C,A)
                    & v2_lattice5(D,C,A)
                    & v3_lattice5(D,C,A)
                    & m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C)))
                        & v19_waybel_0(E,A,k1_lattice5(C))
                        & v20_waybel_0(E,A,k1_lattice5(C))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C))) )
                     => ! [F] :
                          ( ( v1_partfun1(F,C,C)
                            & v3_relat_2(F)
                            & v8_relat_2(F)
                            & m2_relset_1(F,C,C) )
                         => ! [G] :
                              ( ( v1_partfun1(G,C,C)
                                & v3_relat_2(G)
                                & v8_relat_2(G)
                                & m2_relset_1(G,C,C) )
                             => ! [H,I] :
                                  ~ ( E = k5_lattice5(C,A,D)
                                    & C = k3_tarski(a_2_0_lattice8(A,B))
                                    & D = k3_tarski(a_2_1_lattice8(A,B))
                                    & r2_hidden(F,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
                                    & r2_hidden(G,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E)))
                                    & r2_hidden(k4_tarski(H,I),k5_eqrel_1(C,F,G))
                                    & ! [J] :
                                        ( ( ~ v1_xboole_0(J)
                                          & m2_finseq_1(J,C) )
                                       => ~ ( k3_finseq_1(J) = k1_nat_1(np__2,np__2)
                                            & r1_lattice5(C,J,H,I,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_2_0_lattice8,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & m1_lattice8(C,u1_struct_0(B),B,k17_lattice5(B)) )
     => ( r2_hidden(A,a_2_0_lattice8(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k1_mcart_1(k1_funct_1(C,D)) ) ) ) )).

fof(fraenkel_a_2_1_lattice8,axiom,(
    ! [A,B,C] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_yellow11(B)
        & l1_orders_2(B)
        & m1_lattice8(C,u1_struct_0(B),B,k17_lattice5(B)) )
     => ( r2_hidden(A,a_2_1_lattice8(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_mcart_1(k1_funct_1(C,D)) ) ) ) )).
%------------------------------------------------------------------------------