SET007 Axioms: SET007+815.ax


%------------------------------------------------------------------------------
% File     : SET007+815 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Class of Series-Parallel Graphs.  Part III
% 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    : neckla_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   66 (   4 unit)
%            Number of atoms       :  402 (  35 equality)
%            Maximal formula depth :   18 (   7 average)
%            Number of connectives :  403 (  67 ~  ;   8  |; 183  &)
%                                         (   8 <=>; 137 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   0 propositional; 1-4 arity)
%            Number of functors    :   38 (   8 constant; 0-8 arity)
%            Number of variables   :  153 (   0 singleton; 151 !;   2 ?)
%            Maximal term depth    :    5 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_neckla_3,axiom,(
    ! [A,B] :
      ( ( v1_realset1(A)
        & v1_realset1(B) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( v1_finset_1(C)
            & v1_realset1(C) ) ) ) )).

fof(cc2_neckla_3,axiom,(
    ! [A] :
      ( v1_realset1(A)
     => ! [B] :
          ( m1_relset_1(B,A,A)
         => ( v1_relat_2(B)
            & v3_relat_2(B)
            & v7_relat_2(B)
            & v8_relat_2(B)
            & v1_finset_1(B)
            & v1_realset1(B) ) ) ) )).

fof(rc1_neckla_3,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v1_necklace(A)
      & v3_necklace(A)
      & v6_group_1(A) ) )).

fof(cc3_neckla_3,axiom,(
    ! [A] :
      ( ( v3_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v3_necklace(B)
              & v4_yellow_0(B,A) ) ) ) ) )).

fof(cc4_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
           => ( v1_necklace(B)
              & v4_yellow_0(B,A) ) ) ) ) )).

fof(fc1_neckla_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k1_neckla_2(A,B))
        & v1_orders_2(k1_neckla_2(A,B)) ) ) )).

fof(fc2_neckla_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k2_neckla_2(A,B))
        & v1_orders_2(k2_neckla_2(A,B)) ) ) )).

fof(fc3_neckla_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k1_neckla_2(A,B))
        & v1_orders_2(k1_neckla_2(A,B)) ) ) )).

fof(fc4_neckla_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k2_neckla_2(A,B))
        & v1_orders_2(k2_neckla_2(A,B)) ) ) )).

fof(fc5_neckla_3,axiom,(
    ! [A,B] :
      ( ( v6_group_1(A)
        & l1_orders_2(A)
        & v6_group_1(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k1_neckla_2(A,B))
        & v6_group_1(k1_neckla_2(A,B)) ) ) )).

fof(fc6_neckla_3,axiom,(
    ! [A,B] :
      ( ( v6_group_1(A)
        & l1_orders_2(A)
        & v6_group_1(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k2_neckla_2(A,B))
        & v6_group_1(k2_neckla_2(A,B)) ) ) )).

fof(fc7_neckla_3,axiom,(
    ! [A,B] :
      ( ( v1_necklace(A)
        & l1_orders_2(A)
        & v1_necklace(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k1_neckla_2(A,B))
        & v1_necklace(k1_neckla_2(A,B)) ) ) )).

fof(fc8_neckla_3,axiom,(
    ! [A,B] :
      ( ( v1_necklace(A)
        & l1_orders_2(A)
        & v1_necklace(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k2_neckla_2(A,B))
        & v1_necklace(k2_neckla_2(A,B)) ) ) )).

fof(fc9_neckla_3,axiom,(
    ! [A,B] :
      ( ( v3_necklace(A)
        & l1_orders_2(A)
        & v3_necklace(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k1_neckla_2(A,B))
        & v3_necklace(k1_neckla_2(A,B)) ) ) )).

fof(fc10_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_orders_2(k3_necklace(A))
        & v3_necklace(k3_necklace(A)) ) ) )).

fof(fc11_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k3_necklace(A))
        & v1_necklace(k3_necklace(A))
        & v3_necklace(k3_necklace(A)) ) ) )).

fof(cc5_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v1_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v1_neckla_2(A) ) ) ) )).

fof(cc6_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_neckla_3(A) ) ) )).

fof(cc7_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v16_waybel_0(A) )
       => ( ~ v3_struct_0(A)
          & v1_neckla_3(A) ) ) ) )).

fof(cc8_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v1_neckla_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v16_waybel_0(A)
          & v1_neckla_3(A) ) ) ) )).

fof(fc12_neckla_3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_neckla_3(A,B)) ) )).

fof(t1_neckla_3,axiom,(
    ! [A,B] : k2_partfun1(A,A,k6_partfun1(A),B) = k3_xboole_0(k6_partfun1(A),k2_zfmisc_1(B,B)) )).

fof(t2_neckla_3,axiom,(
    ! [A,B,C,D] : k6_partfun1(k2_enumset1(A,B,C,D)) = k2_enumset1(k4_tarski(A,A),k4_tarski(B,B),k4_tarski(C,C),k4_tarski(D,D)) )).

fof(t3_neckla_3,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_zfmisc_1(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) = k2_xboole_0(k6_enumset1(k4_tarski(A,E),k4_tarski(A,F),k4_tarski(B,E),k4_tarski(B,F),k4_tarski(A,G),k4_tarski(A,H),k4_tarski(B,G),k4_tarski(B,H)),k6_enumset1(k4_tarski(C,E),k4_tarski(C,F),k4_tarski(D,E),k4_tarski(D,F),k4_tarski(C,G),k4_tarski(C,H),k4_tarski(D,G),k4_tarski(D,H))) )).

fof(t4_neckla_3,axiom,(
    ! [A] :
      ( v1_realset1(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ~ ( ~ v1_xboole_0(B)
              & ! [C] : B != k1_tarski(k4_tarski(C,C)) ) ) ) )).

fof(t5_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => r3_relat_2(B,A) ) ) )).

fof(t6_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ~ ( k1_card_1(u1_struct_0(A)) = np__2
          & ! [B,C] :
              ~ ( u1_struct_0(A) = k2_tarski(B,C)
                & ( u1_orders_2(A) = k2_tarski(k4_tarski(B,C),k4_tarski(C,B))
                  | u1_orders_2(A) = k1_xboole_0 ) ) ) ) )).

fof(t7_neckla_3,axiom,(
    ! [A] :
      ( ( v3_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v3_necklace(B)
            & l1_orders_2(B) )
         => ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
           => v3_necklace(k2_neckla_2(A,B)) ) ) ) )).

fof(t8_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( k1_neckla_2(A,B) = k1_neckla_2(B,A)
            & k2_neckla_2(A,B) = k2_neckla_2(B,A) ) ) ) )).

fof(t9_neckla_3,axiom,(
    ! [A] :
      ( ( v3_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( l1_orders_2(C)
             => ( ( A = k1_neckla_2(B,C)
                  | A = k2_neckla_2(B,C) )
               => ( v3_necklace(B)
                  & v3_necklace(C) ) ) ) ) ) )).

fof(t10_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( l1_orders_2(C)
             => ( r1_xboole_0(u1_struct_0(B),u1_struct_0(C))
               => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) != k1_neckla_2(B,C)
                    & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) != k2_neckla_2(B,C) )
                  | ( v4_yellow_0(B,A)
                    & m1_yellow_0(B,A)
                    & v4_yellow_0(C,A)
                    & m1_yellow_0(C,A) ) ) ) ) ) ) )).

fof(t11_neckla_3,axiom,(
    u1_orders_2(k3_necklace(k4_necklace(np__4))) = k4_enumset1(k4_tarski(np__0,np__2),k4_tarski(np__2,np__0),k4_tarski(np__0,np__3),k4_tarski(np__3,np__0),k4_tarski(np__1,np__3),k4_tarski(np__3,np__1)) )).

fof(t12_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => r1_xboole_0(u1_orders_2(A),u1_orders_2(k3_necklace(A))) ) )).

fof(t13_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => r1_xboole_0(k6_partfun1(u1_struct_0(A)),u1_orders_2(k3_necklace(A))) ) )).

fof(t14_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)) = k2_xboole_0(k3_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A)),u1_orders_2(A)),u1_orders_2(k3_necklace(A))) ) )).

fof(t15_neckla_3,axiom,(
    ! [A] :
      ( ( v1_orders_2(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ( v3_realset2(A)
       => k3_necklace(A) = A ) ) )).

fof(t16_neckla_3,axiom,(
    ! [A] :
      ( ( v1_orders_2(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => k3_necklace(k3_necklace(A)) = A ) )).

fof(t17_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
           => k3_necklace(k1_neckla_2(A,B)) = k2_neckla_2(k3_necklace(A),k3_necklace(B)) ) ) ) )).

fof(t18_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B))
           => k3_necklace(k2_neckla_2(A,B)) = k1_neckla_2(k3_necklace(A),k3_necklace(B)) ) ) ) )).

fof(t19_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => u1_orders_2(k3_necklace(B)) = k2_wellord1(u1_orders_2(k3_necklace(A)),u1_struct_0(k3_necklace(B))) ) ) )).

fof(t20_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_necklace(A)))
             => ( B = C
               => k3_necklace(k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B)))) = k5_yellow_0(k3_necklace(A),k6_subset_1(u1_struct_0(k3_necklace(A)),k2_pre_topc(k3_necklace(A)),k1_struct_0(k3_necklace(A),C))) ) ) ) ) )).

fof(t21_neckla_3,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [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))
                & ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(k4_tarski(D,E),u1_orders_2(A))
                        <=> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),u1_orders_2(B)) ) ) ) )
          <=> r2_necklace(A,B) ) ) ) )).

fof(t22_neckla_3,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) )
         => r3_necklace(B,A) ) ) )).

fof(t23_neckla_3,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) )
         => ( v1_neckla_2(A)
           => v1_neckla_2(B) ) ) ) )).

fof(t24_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ( r3_necklace(k4_necklace(np__4),A)
      <=> r3_necklace(k4_necklace(np__4),k3_necklace(A)) ) ) )).

fof(t25_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ( v1_neckla_2(A)
      <=> v1_neckla_2(k3_necklace(A)) ) ) )).

fof(d1_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_neckla_3(A)
      <=> ! [B,C] :
            ~ ( r2_hidden(B,u1_struct_0(A))
              & r2_hidden(C,u1_struct_0(A))
              & B != C
              & ~ r1_rewrite1(u1_orders_2(A),B,C)
              & ~ r1_rewrite1(u1_orders_2(A),C,B) ) ) ) )).

fof(t26_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(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_rewrite1(u1_orders_2(A),B,C)
               => r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) )).

fof(t27_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( ( r2_hidden(B,u1_struct_0(A))
            & r2_hidden(C,u1_struct_0(A))
            & r1_rewrite1(u1_orders_2(A),B,C) )
         => r1_rewrite1(u1_orders_2(A),C,B) ) ) )).

fof(d2_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & l1_orders_2(A) )
     => ( v1_neckla_3(A)
      <=> ! [B,C] :
            ( ( r2_hidden(B,u1_struct_0(A))
              & r2_hidden(C,u1_struct_0(A)) )
           => ( B = C
              | r1_rewrite1(u1_orders_2(A),B,C) ) ) ) ) )).

fof(d3_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_neckla_3(A,B) = k6_eqrel_1(u1_struct_0(A),k1_msualg_5(u1_struct_0(A),u1_orders_2(A)),B) ) ) )).

fof(t28_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(B,k1_neckla_3(A,B)) ) ) )).

fof(t29_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( r2_hidden(C,k1_neckla_3(A,B))
             => r2_hidden(k4_tarski(B,C),k1_msualg_5(u1_struct_0(A),u1_orders_2(A))) ) ) ) )).

fof(t30_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( C = k1_neckla_3(A,B)
            <=> ! [D] :
                  ( r2_hidden(D,C)
                <=> r2_hidden(k4_tarski(B,D),k1_msualg_5(u1_struct_0(A),u1_orders_2(A))) ) ) ) ) )).

fof(t31_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_necklace(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ~ ( ~ v1_neckla_3(A)
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v1_orders_2(B)
                & v1_necklace(B)
                & v3_necklace(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_orders_2(C)
                    & v1_necklace(C)
                    & v3_necklace(C)
                    & l1_orders_2(C) )
                 => ~ ( r1_subset_1(u1_struct_0(B),u1_struct_0(C))
                      & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k1_neckla_2(B,C) ) ) ) ) ) )).

fof(t32_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_necklace(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ~ ( ~ v1_neckla_3(k3_necklace(A))
          & ! [B] :
              ( ( ~ v3_struct_0(B)
                & v1_orders_2(B)
                & v1_necklace(B)
                & v3_necklace(B)
                & l1_orders_2(B) )
             => ! [C] :
                  ( ( ~ v3_struct_0(C)
                    & v1_orders_2(C)
                    & v1_necklace(C)
                    & v3_necklace(C)
                    & l1_orders_2(C) )
                 => ~ ( r1_subset_1(u1_struct_0(B),u1_struct_0(C))
                      & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k2_neckla_2(B,C) ) ) ) ) ) )).

fof(t33_neckla_3,axiom,(
    ! [A] :
      ( ( v3_necklace(A)
        & l1_orders_2(A) )
     => ( r2_hidden(A,k4_neckla_2)
       => r2_hidden(k3_necklace(A),k4_neckla_2) ) ) )).

fof(t34_neckla_3,axiom,(
    ! [A] :
      ( ( v1_necklace(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ( ( k1_card_1(u1_struct_0(A)) = np__2
          & r2_hidden(u1_struct_0(A),k13_classes2) )
       => r2_hidden(g1_orders_2(u1_struct_0(A),u1_orders_2(A)),k4_neckla_2) ) ) )).

fof(t35_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( r2_hidden(A,k4_neckla_2)
       => v1_necklace(A) ) ) )).

fof(t36_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ~ ( A = k1_neckla_2(B,C)
                          & r1_subset_1(u1_struct_0(B),u1_struct_0(C))
                          & r2_hidden(k4_tarski(D,E),u1_orders_2(A)) ) ) ) ) ) ) )).

fof(t37_neckla_3,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ~ ( A = k2_neckla_2(B,C)
                          & r2_hidden(k4_tarski(D,E),u1_orders_2(k3_necklace(A))) ) ) ) ) ) ) )).

fof(t38_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ~ ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
                      & k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B))) = k1_neckla_2(C,D)
                      & v1_neckla_3(A)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(C))
                         => ~ r2_hidden(k4_tarski(E,B),u1_orders_2(A)) ) ) ) ) ) ) )).

fof(t39_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_necklace(A)
        & v3_necklace(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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( F = k2_enumset1(B,C,D,E)
                              & r2_incproj(B,C,D,E)
                              & r2_hidden(k4_tarski(B,C),u1_orders_2(A))
                              & r2_hidden(k4_tarski(C,D),u1_orders_2(A))
                              & r2_hidden(k4_tarski(D,E),u1_orders_2(A)) )
                           => ( r2_hidden(k4_tarski(B,D),u1_orders_2(A))
                              | r2_hidden(k4_tarski(B,E),u1_orders_2(A))
                              | r2_hidden(k4_tarski(C,E),u1_orders_2(A))
                              | r2_necklace(k4_necklace(np__4),k5_yellow_0(A,F)) ) ) ) ) ) ) ) ) )).

fof(t40_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_necklace(A)
        & v3_necklace(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ( ( r1_subset_1(u1_struct_0(C),u1_struct_0(D))
                      & k5_yellow_0(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k1_struct_0(A,B))) = k1_neckla_2(C,D)
                      & v1_neckla_3(A)
                      & v1_neckla_3(k3_necklace(A)) )
                   => ( v3_realset2(A)
                      | r3_necklace(k4_necklace(np__4),A) ) ) ) ) ) ) )).

fof(t41_neckla_3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_orders_2(A)
        & v1_necklace(A)
        & v3_necklace(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ( ( v1_neckla_2(A)
          & r2_hidden(u1_struct_0(A),k13_classes2) )
       => r2_hidden(g1_orders_2(u1_struct_0(A),u1_orders_2(A)),k4_neckla_2) ) ) )).

fof(dt_k1_neckla_3,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_neckla_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
%------------------------------------------------------------------------------