SET007 Axioms: SET007+483.ax


%------------------------------------------------------------------------------
% File     : SET007+483 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Boolean Posets, Posets
% Version  : [Urb08] axioms.
% English  : Boolean Posets, Posets under Inclusion and Products of Relational
%            Structures

% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   63 (   6 unit)
%            Number of atoms       :  341 (  33 equality)
%            Maximal formula depth :   35 (   7 average)
%            Number of connectives :  330 (  52 ~  ;   0  |; 180  &)
%                                         (   9 <=>;  89 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   42 (   0 propositional; 1-3 arity)
%            Number of functors    :   37 (   1 constant; 0-3 arity)
%            Number of variables   :  119 (   0 singleton; 116 !;   3 ?)
%            Maximal term depth    :    5 (   2 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(fc1_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) )).

fof(fc2_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v14_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v2_yellow_0(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) )).

fof(fc3_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v13_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v1_yellow_0(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A)) ) ) )).

fof(fc4_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k3_lattice3(A))
        & v1_orders_2(k3_lattice3(A))
        & v2_orders_2(k3_lattice3(A))
        & v3_orders_2(k3_lattice3(A))
        & v4_orders_2(k3_lattice3(A))
        & v1_yellow_0(k3_lattice3(A))
        & v2_yellow_0(k3_lattice3(A))
        & v3_yellow_0(k3_lattice3(A))
        & v1_lattice3(k3_lattice3(A))
        & v2_lattice3(k3_lattice3(A))
        & v3_lattice3(k3_lattice3(A)) ) ) )).

fof(fc5_yellow_1,axiom,(
    ! [A] :
      ( v1_orders_2(k2_yellow_1(A))
      & v2_orders_2(k2_yellow_1(A))
      & v3_orders_2(k2_yellow_1(A))
      & v4_orders_2(k2_yellow_1(A)) ) )).

fof(fc6_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k2_yellow_1(A))
        & v1_orders_2(k2_yellow_1(A))
        & v2_orders_2(k2_yellow_1(A))
        & v3_orders_2(k2_yellow_1(A))
        & v4_orders_2(k2_yellow_1(A)) ) ) )).

fof(fc7_yellow_1,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k3_yellow_1(A))
      & v1_orders_2(k3_yellow_1(A))
      & v2_orders_2(k3_yellow_1(A))
      & v3_orders_2(k3_yellow_1(A))
      & v4_orders_2(k3_yellow_1(A)) ) )).

fof(fc8_yellow_1,axiom,(
    ! [A] :
      ( ~ v3_struct_0(k3_yellow_1(A))
      & v1_orders_2(k3_yellow_1(A))
      & v2_orders_2(k3_yellow_1(A))
      & v3_orders_2(k3_yellow_1(A))
      & v4_orders_2(k3_yellow_1(A))
      & v1_yellow_0(k3_yellow_1(A))
      & v2_yellow_0(k3_yellow_1(A))
      & v3_yellow_0(k3_yellow_1(A))
      & v1_lattice3(k3_yellow_1(A))
      & v2_lattice3(k3_yellow_1(A))
      & v3_lattice3(k3_yellow_1(A)) ) )).

fof(fc9_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A)))
        & v1_orders_2(k2_yellow_1(u1_pre_topc(A)))
        & v2_orders_2(k2_yellow_1(u1_pre_topc(A)))
        & v3_orders_2(k2_yellow_1(u1_pre_topc(A)))
        & v4_orders_2(k2_yellow_1(u1_pre_topc(A)))
        & v1_yellow_0(k2_yellow_1(u1_pre_topc(A)))
        & v2_yellow_0(k2_yellow_1(u1_pre_topc(A)))
        & v3_yellow_0(k2_yellow_1(u1_pre_topc(A)))
        & v1_lattice3(k2_yellow_1(u1_pre_topc(A)))
        & v2_lattice3(k2_yellow_1(u1_pre_topc(A)))
        & v3_lattice3(k2_yellow_1(u1_pre_topc(A)))
        & ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) )).

fof(cc1_yellow_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_yellow_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) )).

fof(rc1_yellow_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_yellow_1(B) ) )).

fof(fc10_yellow_1,axiom,(
    ! [A,B] :
      ( l1_orders_2(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B))
        & v1_yellow_1(k2_funcop_1(A,B)) ) ) )).

fof(fc11_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B)) ) ) )).

fof(fc12_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v2_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B))
        & v2_orders_2(k6_yellow_1(A,B)) ) ) )).

fof(fc13_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A))
        & v1_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) )).

fof(fc14_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A))
        & v1_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v2_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v3_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v4_orders_2(k6_yellow_1(k1_xboole_0,A))
        & v1_yellow_0(k6_yellow_1(k1_xboole_0,A))
        & v2_yellow_0(k6_yellow_1(k1_xboole_0,A))
        & v3_yellow_0(k6_yellow_1(k1_xboole_0,A))
        & v1_lattice3(k6_yellow_1(k1_xboole_0,A))
        & v2_lattice3(k6_yellow_1(k1_xboole_0,A))
        & v3_lattice3(k6_yellow_1(k1_xboole_0,A))
        & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) )).

fof(fc15_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B))
        & v3_orders_2(k6_yellow_1(A,B)) ) ) )).

fof(fc16_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B))
        & v4_orders_2(k6_yellow_1(A,B)) ) ) )).

fof(fc17_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B))
        & v4_orders_2(k6_yellow_1(A,B))
        & v2_lattice3(k6_yellow_1(A,B)) ) ) )).

fof(fc18_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k6_yellow_1(A,B))
        & v1_orders_2(k6_yellow_1(A,B))
        & v4_orders_2(k6_yellow_1(A,B))
        & v1_lattice3(k6_yellow_1(A,B)) ) ) )).

fof(d1_yellow_1,axiom,(
    ! [A] : k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A)) )).

fof(t1_yellow_1,axiom,(
    ! [A] :
      ( u1_struct_0(k2_yellow_1(A)) = A
      & u1_orders_2(k2_yellow_1(A)) = k1_yellow_1(A) ) )).

fof(d2_yellow_1,axiom,(
    ! [A] : k3_yellow_1(A) = k3_lattice3(k1_lattice3(A)) )).

fof(t2_yellow_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
         => ( r3_orders_2(k3_yellow_1(A),B,C)
          <=> r1_tarski(B,C) ) ) ) )).

fof(t3_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r3_orders_2(k2_yellow_1(A),B,C)
              <=> r1_tarski(B,C) ) ) ) ) )).

fof(t4_yellow_1,axiom,(
    ! [A] : k3_yellow_1(A) = k2_yellow_1(k1_zfmisc_1(A)) )).

fof(t5_yellow_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v4_yellow_0(k2_yellow_1(B),k3_yellow_1(A))
        & m1_yellow_0(k2_yellow_1(B),k3_yellow_1(A)) ) ) )).

fof(t6_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_lattice3(k2_yellow_1(A))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
               => r1_tarski(k2_xboole_0(B,C),k10_lattice3(k2_yellow_1(A),B,C)) ) ) ) ) )).

fof(t7_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v2_lattice3(k2_yellow_1(A))
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
               => r1_tarski(k11_lattice3(k2_yellow_1(A),B,C),k3_xboole_0(B,C)) ) ) ) ) )).

fof(t8_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r2_hidden(k2_xboole_0(B,C),A)
               => k10_lattice3(k2_yellow_1(A),B,C) = k2_xboole_0(B,C) ) ) ) ) )).

fof(t9_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r2_hidden(k3_xboole_0(B,C),A)
               => k11_lattice3(k2_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) )).

fof(t10_yellow_1,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_orders_2(A,B,C)
                <=> r1_tarski(B,C) ) ) )
       => u1_orders_2(A) = k1_yellow_1(u1_struct_0(A)) ) ) )).

fof(t11_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ! [B,C] :
            ( ( r2_hidden(B,A)
              & r2_hidden(C,A) )
           => r2_hidden(k2_xboole_0(B,C),A) )
       => v1_lattice3(k2_yellow_1(A)) ) ) )).

fof(t12_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ! [B,C] :
            ( ( r2_hidden(B,A)
              & r2_hidden(C,A) )
           => r2_hidden(k3_xboole_0(B,C),A) )
       => v2_lattice3(k2_yellow_1(A)) ) ) )).

fof(t13_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( r2_hidden(k1_xboole_0,A)
       => k3_yellow_0(k2_yellow_1(A)) = k1_xboole_0 ) ) )).

fof(t14_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( r2_hidden(k3_tarski(A),A)
       => k4_yellow_0(k2_yellow_1(A)) = k3_tarski(A) ) ) )).

fof(t15_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v2_yellow_0(k2_yellow_1(A))
       => r2_hidden(k3_tarski(A),A) ) ) )).

fof(t16_yellow_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_yellow_0(k2_yellow_1(A))
       => r2_hidden(k1_setfam_1(A),A) ) ) )).

fof(t17_yellow_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A)))
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k3_yellow_1(A)))
         => ( k13_lattice3(k3_yellow_1(A),B,C) = k2_xboole_0(B,C)
            & k12_lattice3(k3_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) )).

fof(t18_yellow_1,axiom,(
    ! [A] : k3_yellow_0(k3_yellow_1(A)) = k1_xboole_0 )).

fof(t19_yellow_1,axiom,(
    ! [A] : k4_yellow_0(k3_yellow_1(A)) = A )).

fof(t20_yellow_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) )
     => k2_yellow_0(k3_yellow_1(A),B) = k1_setfam_1(B) ) )).

fof(t21_yellow_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))
     => k1_yellow_0(k3_yellow_1(A),B) = k3_tarski(B) ) )).

fof(t22_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A)))))
         => k1_yellow_0(k2_yellow_1(u1_pre_topc(A)),B) = k3_tarski(B) ) ) )).

fof(t23_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k3_yellow_0(k2_yellow_1(u1_pre_topc(A))) = k1_xboole_0 ) )).

fof(t24_yellow_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => k4_yellow_0(k2_yellow_1(u1_pre_topc(A))) = u1_struct_0(A) ) )).

fof(t25_yellow_1,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tops_2(B,A)
          <=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) ) ) ) )).

fof(d3_yellow_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_yellow_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k2_relat_1(A))
           => l1_orders_2(B) ) ) ) )).

fof(d4_yellow_1,axiom,(
    ! [A,B] :
      ( ( v1_yellow_1(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v1_orders_2(C)
            & l1_orders_2(C) )
         => ( C = k5_yellow_1(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r2_hidden(D,k4_card_3(k12_pralg_1(A,B)))
                       => ( r1_orders_2(C,D,E)
                        <=> ? [F] :
                              ( v1_relat_1(F)
                              & v1_funct_1(F)
                              & ? [G] :
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & F = D
                                  & G = E
                                  & ! [H] :
                                      ~ ( r2_hidden(H,A)
                                        & ! [I] :
                                            ( l1_orders_2(I)
                                           => ! [J] :
                                                ( m1_subset_1(J,u1_struct_0(I))
                                               => ! [K] :
                                                    ( m1_subset_1(K,u1_struct_0(I))
                                                   => ~ ( I = k1_funct_1(B,H)
                                                        & J = k1_funct_1(F,H)
                                                        & K = k1_funct_1(G,H)
                                                        & r1_orders_2(I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_yellow_1,axiom,(
    ! [A,B] :
      ( l1_orders_2(B)
     => k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) )).

fof(t26_yellow_1,axiom,(
    ! [A] :
      ( ( v1_yellow_1(A)
        & m1_pboole(A,k1_xboole_0) )
     => k5_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) )).

fof(t27_yellow_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k6_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) )).

fof(t28_yellow_1,axiom,(
    ! [A,B] :
      ( l1_orders_2(B)
     => k1_funct_2(A,u1_struct_0(B)) = u1_struct_0(k6_yellow_1(A,B)) ) )).

fof(d6_yellow_1,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( v1_orders_2(C)
                & v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
                & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) )
             => ( C = k7_yellow_1(A,B)
              <=> ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                   => ( r2_hidden(D,u1_struct_0(C))
                    <=> ( r2_hidden(D,k1_funct_2(u1_struct_0(A),u1_struct_0(B)))
                        & v5_orders_3(D,A,B) ) ) ) ) ) ) ) )).

fof(dt_k1_yellow_1,axiom,(
    ! [A] :
      ( v1_relat_2(k1_yellow_1(A))
      & v4_relat_2(k1_yellow_1(A))
      & v8_relat_2(k1_yellow_1(A))
      & v1_partfun1(k1_yellow_1(A),A,A)
      & m2_relset_1(k1_yellow_1(A),A,A) ) )).

fof(redefinition_k1_yellow_1,axiom,(
    ! [A] : k1_yellow_1(A) = k1_wellord2(A) )).

fof(dt_k2_yellow_1,axiom,(
    ! [A] :
      ( v1_orders_2(k2_yellow_1(A))
      & l1_orders_2(k2_yellow_1(A)) ) )).

fof(dt_k3_yellow_1,axiom,(
    ! [A] :
      ( v1_orders_2(k3_yellow_1(A))
      & l1_orders_2(k3_yellow_1(A)) ) )).

fof(dt_k4_yellow_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_yellow_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => l1_orders_2(k4_yellow_1(A,B,C)) ) )).

fof(redefinition_k4_yellow_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_yellow_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k4_yellow_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k5_yellow_1,axiom,(
    ! [A,B] :
      ( ( v1_yellow_1(B)
        & m1_pboole(B,A) )
     => ( v1_orders_2(k5_yellow_1(A,B))
        & l1_orders_2(k5_yellow_1(A,B)) ) ) )).

fof(dt_k6_yellow_1,axiom,(
    ! [A,B] :
      ( l1_orders_2(B)
     => ( v1_orders_2(k6_yellow_1(A,B))
        & l1_orders_2(k6_yellow_1(A,B)) ) ) )).

fof(dt_k7_yellow_1,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B) )
     => ( v1_orders_2(k7_yellow_1(A,B))
        & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B))
        & m1_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) )).
%------------------------------------------------------------------------------