SET007 Axioms: SET007+636.ax


%------------------------------------------------------------------------------
% File     : SET007+636 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Lim-Inf Convergence
% 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    : waybel28 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   45 (   0 unit)
%            Number of atoms       :  449 (  21 equality)
%            Maximal formula depth :   14 (   9 average)
%            Number of connectives :  469 (  65 ~  ;   0  |; 278  &)
%                                         (   6 <=>; 120 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   37 (   0 propositional; 1-3 arity)
%            Number of functors    :   26 (   0 constant; 1-5 arity)
%            Number of variables   :  121 (   0 singleton; 116 !;   5 ?)
%            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(rc1_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_waybel_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v1_waybel28(B,A) ) ) )).

fof(rc2_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v1_waybel28(B,A) ) ) )).

fof(fc1_waybel28,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_orders_2(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
     => ( ~ v3_struct_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
        & v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
        & v6_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A)
        & v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) ) ) )).

fof(fc2_waybel28,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( ~ v3_struct_0(k1_waybel28(A,B,C))
        & v3_orders_2(k1_waybel28(A,B,C))
        & v6_waybel_0(k1_waybel28(A,B,C),A)
        & v7_waybel_0(k1_waybel28(A,B,C)) ) ) )).

fof(rc3_waybel28,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A) )
     => ? [C] :
          ( m2_yellow_6(C,A,B)
          & ~ v3_struct_0(C)
          & v3_orders_2(C)
          & v6_waybel_0(C,A)
          & v7_waybel_0(C) ) ) )).

fof(t1_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => r3_orders_2(A,k2_waybel_9(A,B),k1_waybel11(A,B)) ) ) )).

fof(t2_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ! [D] :
                    ( m2_yellow_6(D,A,B)
                   => C = k1_waybel11(A,D) )
               => ( C = k1_waybel11(A,B)
                  & ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) ) ) ) )).

fof(t3_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r2_hidden(B,k7_yellow_6(A))
                  & ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => ( r2_hidden(D,k7_yellow_6(A))
                       => C = k1_waybel11(A,D) ) ) )
               => ( C = k1_waybel11(A,B)
                  & ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => ( r2_hidden(D,k7_yellow_6(A))
                       => r1_orders_2(A,k2_waybel_9(A,D),C) ) ) ) ) ) ) ) )).

fof(d1_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v1_waybel28(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_orders_2(A,C,k3_yellow_6(u1_struct_0(A),A,B,C)) ) ) ) ) )).

fof(t4_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => v1_waybel28(k7_grcat_1(A),A) ) )).

fof(t5_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_waybel_0(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_orders_2(A,B,D)
                  & r1_orders_2(A,C,D) ) ) ) ) )).

fof(t6_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_waybel_0(A)
        & l1_orders_2(A) )
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & v1_waybel28(B,A) ) ) )).

fof(d2_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v6_waybel_0(D,A)
                    & l1_waybel_0(D,A) )
                 => ( D = k1_waybel28(A,B,C)
                  <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & u1_waybel_0(A,D) = k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B)) ) ) ) ) ) ) )).

fof(t7_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => u1_struct_0(k1_waybel28(A,B,C)) = u1_struct_0(B) ) ) ) )).

fof(t8_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => k1_waybel28(A,B,C) = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B))) ) ) ) )).

fof(t9_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ( ~ v3_struct_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
                & v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
                & v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C))
                & l1_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A) ) ) ) ) )).

fof(t10_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ( ~ v3_struct_0(k1_waybel28(A,B,C))
                & v3_orders_2(k1_waybel28(A,B,C))
                & v7_waybel_0(k1_waybel28(A,B,C))
                & l1_waybel_0(k1_waybel28(A,B,C),A) ) ) ) ) )).

fof(t11_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ( r2_hidden(B,k7_yellow_6(A))
               => r2_hidden(k1_waybel28(A,B,C),k7_yellow_6(A)) ) ) ) ) )).

fof(t12_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_orders_2(C)
                & v7_waybel_0(C)
                & l1_waybel_0(C,A) )
             => ( g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) = g1_waybel_0(A,u1_struct_0(C),u1_orders_2(C),u1_waybel_0(A,C))
               => m2_yellow_6(C,A,B) ) ) ) ) )).

fof(t13_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & v1_waybel28(C,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => m2_yellow_6(k1_waybel28(A,B,C),A,B) ) ) ) )).

fof(t14_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r2_hidden(B,k7_yellow_6(A))
                  & C = k1_waybel11(A,B)
                  & ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => ( r2_hidden(D,k7_yellow_6(A))
                       => r1_orders_2(A,k2_waybel_9(A,D),C) ) ) )
               => ( C = k1_waybel11(A,B)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
                        & v1_waybel28(D,B)
                        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
                     => r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,B,D)),C) ) ) ) ) ) ) )).

fof(t15_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( C = k1_waybel11(A,B)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
                        & v1_waybel28(D,B)
                        & m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
                     => r1_orders_2(A,k2_waybel_9(A,k2_waybel28(A,B,D)),C) ) )
               => ! [D] :
                    ( m2_yellow_6(D,A,B)
                   => C = k1_waybel11(A,D) ) ) ) ) ) )).

fof(d3_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m4_yellow_6(B,A)
         => ( B = k3_waybel28(A)
          <=> ! [C] :
                ( ( ~ v3_struct_0(C)
                  & v3_orders_2(C)
                  & v7_waybel_0(C)
                  & l1_waybel_0(C,A) )
               => ( r2_hidden(C,k7_yellow_6(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_hidden(k4_tarski(C,D),B)
                      <=> ! [E] :
                            ( m2_yellow_6(E,A,C)
                           => D = k1_waybel11(A,E) ) ) ) ) ) ) ) ) )).

fof(t16_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(B,k7_yellow_6(A))
               => ( r2_hidden(k4_tarski(B,C),k3_waybel28(A))
                <=> ! [D] :
                      ( m2_yellow_6(D,A,B)
                     => ( r2_hidden(D,k7_yellow_6(A))
                       => C = k1_waybel11(A,D) ) ) ) ) ) ) ) )).

fof(t17_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_orders_2(B)
            & v7_waybel_0(B)
            & v1_yellow_6(B,A)
            & l1_waybel_0(B,A) )
         => ! [C] :
              ( m2_yellow_6(C,A,B)
             => ( v1_yellow_6(C,A)
                & k5_yellow_6(A,B) = k5_yellow_6(A,C) ) ) ) ) )).

fof(d4_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => k4_waybel28(A) = u1_pre_topc(k14_yellow_6(A,k3_waybel28(A))) ) )).

fof(t18_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => v4_yellow_6(k3_waybel28(A),A) ) )).

fof(t19_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => v5_yellow_6(k3_waybel28(A),A) ) )).

fof(t20_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => v6_yellow_6(k3_waybel28(A),A) ) )).

fof(t21_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( r2_hidden(k4_tarski(B,C),k3_waybel28(A))
         => r2_hidden(B,k7_yellow_6(A)) ) ) )).

fof(t22_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( m4_yellow_6(B,A)
         => ! [C] :
              ( m4_yellow_6(C,A)
             => ( r1_tarski(B,C)
               => r1_tarski(u1_pre_topc(k14_yellow_6(A,C)),u1_pre_topc(k14_yellow_6(A,B))) ) ) ) ) )).

fof(t23_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => r1_tarski(k3_waybel28(A),k2_waybel11(A)) ) )).

fof(t24_waybel28,axiom,(
    ! [A,B] :
      ( r1_tarski(A,B)
     => r2_hidden(A,k2_yellow_6(B)) ) )).

fof(t25_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k4_waybel17(A,B),k7_yellow_6(A)) ) ) )).

fof(t26_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( m2_yellow_6(C,A,k4_waybel17(A,B))
             => k1_waybel11(A,C) = k1_yellow_0(A,B) ) ) ) )).

fof(t27_waybel28,axiom,(
    ! [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)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k4_tarski(k4_waybel17(A,B),k1_yellow_0(A,B)),k3_waybel28(A)) ) ) )).

fof(t28_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k4_waybel28(A))
           => v3_waybel11(B,A) ) ) ) )).

fof(t29_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_hidden(B,k5_waybel11(A))
           => r2_hidden(B,k4_waybel28(A)) ) ) ) )).

fof(t30_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v13_waybel_0(B,A)
              & r2_hidden(B,k4_waybel28(A)) )
           => r2_hidden(B,k5_waybel11(A)) ) ) ) )).

fof(t31_waybel28,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
           => ( r2_hidden(k3_subset_1(u1_struct_0(A),B),k4_waybel28(A))
            <=> v2_waybel11(B,A) ) ) ) ) )).

fof(dt_k1_waybel28,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( ~ v3_struct_0(k1_waybel28(A,B,C))
        & v6_waybel_0(k1_waybel28(A,B,C),A)
        & l1_waybel_0(k1_waybel28(A,B,C),A) ) ) )).

fof(dt_k2_waybel28,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & v1_waybel28(C,B)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => ( v6_waybel_0(k2_waybel28(A,B,C),A)
        & m2_yellow_6(k2_waybel28(A,B,C),A,B) ) ) )).

fof(redefinition_k2_waybel28,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v7_waybel_0(B)
        & l1_waybel_0(B,A)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
        & v1_waybel28(C,B)
        & m1_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
     => k2_waybel28(A,B,C) = k1_waybel28(A,B,C) ) )).

fof(dt_k3_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m4_yellow_6(k3_waybel28(A),A) ) )).

fof(dt_k4_waybel28,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => m1_subset_1(k4_waybel28(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
%------------------------------------------------------------------------------