SET007 Axioms: SET007+480.ax


%------------------------------------------------------------------------------
% File     : SET007+480 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Bounds in Posets and Relational Substructures
% 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    : yellow_0 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  117 (   0 unit)
%            Number of atoms       :  919 (  72 equality)
%            Maximal formula depth :   18 (   9 average)
%            Number of connectives :  873 (  71 ~  ;   2  |; 362  &)
%                                         (  34 <=>; 404 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   0 propositional; 1-3 arity)
%            Number of functors    :   27 (   2 constant; 0-3 arity)
%            Number of variables   :  344 (   0 singleton; 331 !;  13 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) )).

fof(cc2_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v3_lattice3(A) ) ) ) )).

fof(fc1_yellow_0,axiom,(
    ! [A,B] :
      ( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
     => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B))
        & v1_orders_2(g1_orders_2(k1_tarski(A),B))
        & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) )).

fof(rc1_yellow_0,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_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v3_realset2(A) ) )).

fof(fc2_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) )).

fof(cc3_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v3_yellow_0(A) ) ) ) )).

fof(cc4_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_yellow_0(A)
       => ( v1_yellow_0(A)
          & v2_yellow_0(A) ) ) ) )).

fof(cc5_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v1_yellow_0(A)
          & v2_yellow_0(A) )
       => v3_yellow_0(A) ) ) )).

fof(rc2_yellow_0,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A) ) )).

fof(rc3_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ? [B] :
          ( m1_yellow_0(B,A)
          & v1_orders_2(B)
          & v4_yellow_0(B,A) ) ) )).

fof(rc4_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_0(B,A)
          & ~ v3_struct_0(B)
          & v1_orders_2(B)
          & v4_yellow_0(B,A) ) ) )).

fof(cc6_yellow_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v2_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) )).

fof(cc7_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v3_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) )).

fof(cc8_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v4_orders_2(B)
              & v4_yellow_0(B,A) ) ) ) ) )).

fof(cc9_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v7_yellow_0(B,A)
           => v5_yellow_0(B,A) ) ) ) )).

fof(cc10_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v8_yellow_0(B,A)
           => v6_yellow_0(B,A) ) ) ) )).

fof(rc5_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_yellow_0(B,A)
          & ~ v3_struct_0(B)
          & v1_orders_2(B)
          & v4_yellow_0(B,A)
          & v5_yellow_0(B,A)
          & v6_yellow_0(B,A)
          & v7_yellow_0(B,A)
          & v8_yellow_0(B,A) ) ) )).

fof(cc11_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( ( ~ v3_struct_0(B)
              & v4_yellow_0(B,A)
              & v5_yellow_0(B,A) )
           => ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v2_lattice3(B)
              & v4_yellow_0(B,A)
              & v5_yellow_0(B,A) ) ) ) ) )).

fof(cc12_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( ( ~ v3_struct_0(B)
              & v4_yellow_0(B,A)
              & v6_yellow_0(B,A) )
           => ( ~ v3_struct_0(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v4_yellow_0(B,A)
              & v6_yellow_0(B,A) ) ) ) ) )).

fof(d1_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v2_orders_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => r1_orders_2(A,B,B) ) ) ) )).

fof(d2_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_orders_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,C,D) )
                     => r1_orders_2(A,B,D) ) ) ) ) ) ) )).

fof(d3_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v4_orders_2(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ( r1_orders_2(A,B,C)
                    & r1_orders_2(A,C,B) )
                 => B = C ) ) ) ) ) )).

fof(t1_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( ( C = E
                                & D = F )
                             => ( ( r1_orders_2(A,C,D)
                                 => r1_orders_2(B,E,F) )
                                & ( r2_orders_2(A,C,D)
                                 => r2_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C,D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                   => ( D = E
                     => ( ( r2_lattice3(A,C,D)
                         => r2_lattice3(B,C,E) )
                        & ( r1_lattice3(A,C,D)
                         => r1_lattice3(B,C,E) ) ) ) ) ) ) ) ) )).

fof(t3_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v3_lattice3(A) )
           => v3_lattice3(B) ) ) ) )).

fof(t4_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
               => ! [D] :
                    ( ( r1_lattice3(A,D,C)
                     => r1_lattice3(A,D,B) )
                    & ( r2_lattice3(A,D,B)
                     => r2_lattice3(A,D,C) ) ) ) ) ) ) )).

fof(t5_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( ( r2_lattice3(A,B,C)
             => r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
            & ( r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
             => r2_lattice3(A,B,C) )
            & ( r1_lattice3(A,B,C)
             => r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
            & ( r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
             => r1_lattice3(A,B,C) ) ) ) ) )).

fof(t6_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_lattice3(A,k1_xboole_0,B)
            & r1_lattice3(A,k1_xboole_0,B) ) ) ) )).

fof(t7_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_lattice3(A,k1_tarski(C),B)
                 => r1_orders_2(A,B,C) )
                & ( r1_orders_2(A,B,C)
                 => r1_lattice3(A,k1_tarski(C),B) )
                & ( r2_lattice3(A,k1_tarski(C),B)
                 => r1_orders_2(A,C,B) )
                & ( r1_orders_2(A,C,B)
                 => r2_lattice3(A,k1_tarski(C),B) ) ) ) ) ) )).

fof(t8_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) ) )
                    & ( ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) )
                     => r1_lattice3(A,k2_tarski(C,D),B) )
                    & ( r2_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) ) )
                    & ( ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) )
                     => r2_lattice3(A,k2_tarski(C,D),B) ) ) ) ) ) ) )).

fof(t9_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( r1_tarski(B,C)
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r1_lattice3(A,C,D)
                 => r1_lattice3(A,B,D) )
                & ( r2_lattice3(A,C,D)
                 => r2_lattice3(A,B,D) ) ) ) ) ) )).

fof(t10_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C,D] :
          ( m1_subset_1(D,u1_struct_0(A))
         => ( ( ( r1_lattice3(A,B,D)
                & r1_lattice3(A,C,D) )
             => r1_lattice3(A,k2_xboole_0(B,C),D) )
            & ( ( r2_lattice3(A,B,D)
                & r2_lattice3(A,C,D) )
             => r2_lattice3(A,k2_xboole_0(B,C),D) ) ) ) ) )).

fof(t11_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r2_lattice3(A,B,C)
                  & r1_orders_2(A,C,D) )
               => r2_lattice3(A,B,D) ) ) ) ) )).

fof(t12_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r1_lattice3(A,B,C)
                  & r1_orders_2(A,D,C) )
               => r1_lattice3(A,B,D) ) ) ) ) )).

fof(d4_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_yellow_0(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & r1_lattice3(A,u1_struct_0(A),B) ) ) ) )).

fof(d5_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_yellow_0(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & r2_lattice3(A,u1_struct_0(A),B) ) ) ) )).

fof(d6_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_yellow_0(A)
      <=> ( v1_yellow_0(A)
          & v2_yellow_0(A) ) ) ) )).

fof(t13_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ( ( v1_yellow_0(A)
               => v1_yellow_0(B) )
              & ( v2_yellow_0(A)
               => v2_yellow_0(B) ) ) ) ) ) )).

fof(d7_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( r1_yellow_0(A,B)
        <=> ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_lattice3(A,B,C)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_lattice3(A,B,D)
                   => r1_orders_2(A,C,D) ) )
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_lattice3(A,B,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_lattice3(A,B,E)
                           => r1_orders_2(A,D,E) ) ) )
                   => D = C ) ) ) ) ) )).

fof(d8_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( r2_yellow_0(A,B)
        <=> ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) )
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_lattice3(A,B,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r1_lattice3(A,B,E)
                           => r1_orders_2(A,E,D) ) ) )
                   => D = C ) ) ) ) ) )).

fof(t14_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] :
                ( ( r1_yellow_0(A,C)
                 => r1_yellow_0(B,C) )
                & ( r2_yellow_0(A,C)
                 => r2_yellow_0(B,C) ) ) ) ) ) )).

fof(t15_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( r1_yellow_0(A,B)
        <=> ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_lattice3(A,B,C)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_lattice3(A,B,D)
                   => r1_orders_2(A,C,D) ) ) ) ) ) )).

fof(t16_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( r2_yellow_0(A,B)
        <=> ? [C] :
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) ) ) ) ) )).

fof(t17_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( r1_yellow_0(A,B)
          & r2_yellow_0(A,B) ) ) )).

fof(t18_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( ( D = k10_lattice3(A,B,C)
                        & r1_yellow_0(A,k2_tarski(B,C)) )
                     => ( r1_orders_2(A,B,D)
                        & r1_orders_2(A,C,D)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,B,E)
                                & r1_orders_2(A,C,E) )
                             => r1_orders_2(A,D,E) ) ) ) )
                    & ( ( r1_orders_2(A,B,D)
                        & r1_orders_2(A,C,D)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,B,E)
                                & r1_orders_2(A,C,E) )
                             => r1_orders_2(A,D,E) ) ) )
                     => ( D = k10_lattice3(A,B,C)
                        & r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) )).

fof(t19_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( ( D = k11_lattice3(A,B,C)
                        & r2_yellow_0(A,k2_tarski(B,C)) )
                     => ( r1_orders_2(A,D,B)
                        & r1_orders_2(A,D,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,E,B)
                                & r1_orders_2(A,E,C) )
                             => r1_orders_2(A,E,D) ) ) ) )
                    & ( ( r1_orders_2(A,D,B)
                        & r1_orders_2(A,D,C)
                        & ! [E] :
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,E,B)
                                & r1_orders_2(A,E,C) )
                             => r1_orders_2(A,E,D) ) ) )
                     => ( D = k11_lattice3(A,B,C)
                        & r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) )).

fof(t20_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_lattice3(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) )).

fof(t21_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_lattice3(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) )).

fof(t22_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k13_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,B,D)
                      & r1_orders_2(A,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,B,E)
                              & r1_orders_2(A,C,E) )
                           => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).

fof(t23_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(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] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k12_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) )).

fof(t24_yellow_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = k13_lattice3(A,B,C)
              <=> r1_orders_2(A,C,B) ) ) ) ) )).

fof(t25_yellow_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(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))
             => ( B = k12_lattice3(A,B,C)
              <=> r3_orders_2(A,B,C) ) ) ) ) )).

fof(d9_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_yellow_0(A,B)
           => ( C = k1_yellow_0(A,B)
            <=> ( r2_lattice3(A,B,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,B,D)
                     => r1_orders_2(A,C,D) ) ) ) ) ) ) ) )).

fof(d10_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_yellow_0(A,B)
           => ( C = k2_yellow_0(A,B)
            <=> ( r1_lattice3(A,B,C)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,B,D)
                     => r1_orders_2(A,D,C) ) ) ) ) ) ) ) )).

fof(t26_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] :
                ( r1_yellow_0(A,C)
               => k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) )).

fof(t27_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] :
                ( r2_yellow_0(A,C)
               => k2_yellow_0(A,C) = k2_yellow_0(B,C) ) ) ) ) )).

fof(t28_yellow_0,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] :
          ( k1_yellow_0(A,B) = k15_lattice3(k14_lattice3(A),B)
          & k2_yellow_0(A,B) = k16_lattice3(k14_lattice3(A),B) ) ) )).

fof(t29_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] :
          ( k15_lattice3(A,B) = k1_yellow_0(k3_lattice3(A),B)
          & k16_lattice3(A,B) = k2_yellow_0(k3_lattice3(A),B) ) ) )).

fof(t30_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ( B = k1_yellow_0(A,C)
                  & r1_yellow_0(A,C) )
               => ( r2_lattice3(A,C,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_lattice3(A,C,D)
                       => r1_orders_2(A,B,D) ) ) ) )
              & ( ( r2_lattice3(A,C,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_lattice3(A,C,D)
                       => r1_orders_2(A,B,D) ) ) )
               => ( B = k1_yellow_0(A,C)
                  & r1_yellow_0(A,C) ) ) ) ) ) )).

fof(t31_yellow_0,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) )
               => ( r1_lattice3(A,C,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) ) )
              & ( ( r1_lattice3(A,C,B)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) )
               => ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) ) ) ) ) ) )).

fof(t32_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( B = k1_yellow_0(A,C)
            <=> ( r2_lattice3(A,C,B)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,C,D)
                     => r1_orders_2(A,B,D) ) ) ) ) ) ) )).

fof(t33_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( B = k2_yellow_0(A,C)
            <=> ( r1_lattice3(A,C,B)
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,C,D)
                     => r1_orders_2(A,D,B) ) ) ) ) ) ) )).

fof(t34_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( ( r1_tarski(B,C)
            & r1_yellow_0(A,B)
            & r1_yellow_0(A,C) )
         => r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) )).

fof(t35_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B,C] :
          ( ( r1_tarski(B,C)
            & r2_yellow_0(A,B)
            & r2_yellow_0(A,C) )
         => r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)) ) ) )).

fof(t36_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r1_yellow_0(A,B)
            & r1_yellow_0(A,C)
            & r1_yellow_0(A,k2_xboole_0(B,C)) )
         => k1_yellow_0(A,k2_xboole_0(B,C)) = k10_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) )).

fof(t37_yellow_0,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r2_yellow_0(A,B)
            & r2_yellow_0(A,C)
            & r2_yellow_0(A,k2_xboole_0(B,C)) )
         => k2_yellow_0(A,k2_xboole_0(B,C)) = k11_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) )).

fof(t38_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r1_yellow_0(A,k1_struct_0(A,B))
            & r2_yellow_0(A,k1_struct_0(A,B)) ) ) ) )).

fof(t39_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k1_yellow_0(A,k1_struct_0(A,B)) = B
            & k2_yellow_0(A,k1_struct_0(A,B)) = B ) ) ) )).

fof(t40_yellow_0,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_yellow_0(A,k2_struct_0(A,B,C)) = k12_lattice3(A,B,C) ) ) ) )).

fof(t41_yellow_0,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_0(A,k2_struct_0(A,B,C)) = k13_lattice3(A,B,C) ) ) ) )).

fof(t42_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( r1_yellow_0(A,k1_xboole_0)
        & r2_yellow_0(A,u1_struct_0(A)) ) ) )).

fof(t43_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( r2_yellow_0(A,k1_xboole_0)
        & r1_yellow_0(A,u1_struct_0(A)) ) ) )).

fof(d11_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k3_yellow_0(A) = k1_yellow_0(A,k1_xboole_0) ) )).

fof(d12_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0) ) )).

fof(t44_yellow_0,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))
         => r1_orders_2(A,k3_yellow_0(A),B) ) ) )).

fof(t45_yellow_0,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))
         => r1_orders_2(A,B,k4_yellow_0(A)) ) ) )).

fof(t46_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                <=> r2_lattice3(A,C,D) ) )
            & r1_yellow_0(A,B) )
         => r1_yellow_0(A,C) ) ) )).

fof(t47_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r1_yellow_0(A,B)
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                <=> r2_lattice3(A,C,D) ) ) )
         => k1_yellow_0(A,B) = k1_yellow_0(A,C) ) ) )).

fof(t48_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r1_lattice3(A,B,D)
                <=> r1_lattice3(A,C,D) ) )
            & r2_yellow_0(A,B) )
         => r2_yellow_0(A,C) ) ) )).

fof(t49_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r2_yellow_0(A,B)
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r1_lattice3(A,B,D)
                <=> r1_lattice3(A,C,D) ) ) )
         => k2_yellow_0(A,B) = k2_yellow_0(A,C) ) ) )).

fof(t50_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( r1_yellow_0(A,B)
           => r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
          & ( r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
           => r1_yellow_0(A,B) )
          & ( r2_yellow_0(A,B)
           => r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
          & ( r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
           => r2_yellow_0(A,B) ) ) ) )).

fof(t51_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( r1_yellow_0(A,B)
            | r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
         => k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) )).

fof(t52_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( r2_yellow_0(A,B)
            | r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
         => k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) )).

fof(t53_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r1_yellow_0(A,B) )
       => v3_lattice3(A) ) ) )).

fof(t54_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_lattice3(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_finset_1(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r1_yellow_0(A,B) ) ) ) )).

fof(t55_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_lattice3(A)
      <=> ! [B] :
            ( ( ~ v1_xboole_0(B)
              & v1_finset_1(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r2_yellow_0(A,B) ) ) ) )).

fof(t56_yellow_0,axiom,(
    ! [A,B] :
      ( m2_relset_1(B,A,A)
     => B = k1_toler_1(B,A) ) )).

fof(d13_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( m1_yellow_0(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) )).

fof(d14_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
          <=> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B)) ) ) ) )).

fof(t57_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A)
            & m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) ) ) ) )).

fof(t58_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( ( v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) ) ) ) ) )).

fof(d15_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_orders_2(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( C = k5_yellow_0(A,B)
              <=> u1_struct_0(C) = B ) ) ) ) )).

fof(t59_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).

fof(t60_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = C
                              & F = D
                              & r1_orders_2(B,E,F) )
                           => r1_orders_2(A,C,D) ) ) ) ) ) ) ) )).

fof(t61_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = C
                              & F = D
                              & r1_orders_2(A,C,D)
                              & r2_hidden(E,u1_struct_0(B))
                              & r2_hidden(F,u1_struct_0(B)) )
                           => r1_orders_2(B,E,F) ) ) ) ) ) ) ) )).

fof(t62_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C,D] :
              ( m1_subset_1(D,u1_struct_0(A))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => ( E = D
                   => ( ( r1_lattice3(A,C,D)
                       => r1_lattice3(B,C,E) )
                      & ( r2_lattice3(A,C,D)
                       => r2_lattice3(B,C,E) ) ) ) ) ) ) ) )).

fof(t63_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( E = D
                       => ( ( r1_lattice3(B,C,E)
                           => r1_lattice3(A,C,D) )
                          & ( r2_lattice3(B,C,E)
                           => r2_lattice3(A,C,D) ) ) ) ) ) ) ) ) )).

fof(d16_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v5_yellow_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,u1_struct_0(B))
                        & r2_hidden(D,u1_struct_0(B))
                        & r2_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) )).

fof(d17_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v6_yellow_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,u1_struct_0(B))
                        & r2_hidden(D,u1_struct_0(B))
                        & r1_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) )).

fof(d18_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v7_yellow_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => ( r2_yellow_0(A,C)
                 => r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) )).

fof(d19_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v8_yellow_0(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => ( r1_yellow_0(A,C)
                 => r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) )).

fof(t64_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( r2_yellow_0(A,C)
                  & r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) )
               => ( r2_yellow_0(B,C)
                  & k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) )).

fof(t65_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( r1_yellow_0(A,C)
                  & r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) )
               => ( r1_yellow_0(B,C)
                  & k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) )).

fof(t66_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r2_yellow_0(A,k2_struct_0(B,C,D))
                      & r2_hidden(k2_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
                   => ( r2_yellow_0(B,k2_struct_0(B,C,D))
                      & k2_yellow_0(B,k2_struct_0(B,C,D)) = k2_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) )).

fof(t67_yellow_0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r1_yellow_0(A,k2_struct_0(B,C,D))
                      & r2_hidden(k1_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
                   => ( r1_yellow_0(B,k2_struct_0(B,C,D))
                      & k1_yellow_0(B,k2_struct_0(B,C,D)) = k1_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) )).

fof(t68_yellow_0,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] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(k2_yellow_0(A,C),u1_struct_0(B))
               => k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) )).

fof(t69_yellow_0,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] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(k1_yellow_0(A,C),u1_struct_0(B))
               => k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) )).

fof(t70_yellow_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( E = C
                              & F = D )
                           => k12_lattice3(B,C,D) = k12_lattice3(A,E,F) ) ) ) ) ) ) ) )).

fof(t71_yellow_0,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v6_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( E = C
                              & F = D )
                           => k13_lattice3(B,C,D) = k13_lattice3(A,E,F) ) ) ) ) ) ) ) )).

fof(s1_yellow_0,axiom,(
    ? [A] :
      ( ~ v3_struct_0(A)
      & v1_orders_2(A)
      & l1_orders_2(A)
      & u1_struct_0(A) = f1_s1_yellow_0
      & ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
              <=> p1_s1_yellow_0(B,C) ) ) ) ) )).

fof(dt_m1_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_yellow_0(B,A)
         => l1_orders_2(B) ) ) )).

fof(existence_m1_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ? [B] : m1_yellow_0(B,A) ) )).

fof(dt_k1_yellow_0,axiom,(
    ! [A,B] :
      ( l1_orders_2(A)
     => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) )).

fof(dt_k2_yellow_0,axiom,(
    ! [A,B] :
      ( l1_orders_2(A)
     => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) )).

fof(dt_k3_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) )).

fof(dt_k4_yellow_0,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => m1_subset_1(k4_yellow_0(A),u1_struct_0(A)) ) )).

fof(dt_k5_yellow_0,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_orders_2(k5_yellow_0(A,B))
        & v4_yellow_0(k5_yellow_0(A,B),A)
        & m1_yellow_0(k5_yellow_0(A,B),A) ) ) )).
%------------------------------------------------------------------------------