SET007 Axioms: SET007+494.ax


%------------------------------------------------------------------------------
% File     : SET007+494 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Equational Characterization of Continuous Lattices
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : waybel_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   2 unit)
%            Number of atoms       :  675 (  47 equality)
%            Maximal formula depth :   22 (  11 average)
%            Number of connectives :  691 (  78 ~  ;   0  |; 414  &)
%                                         (  11 <=>; 188 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   47 (   0 propositional; 1-4 arity)
%            Number of functors    :   42 (   0 constant; 1-6 arity)
%            Number of variables   :  241 (   0 singleton; 228 !;  13 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_waybel_5,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m1_subset_1(E,A) )
     => ~ v1_xboole_0(k2_relat_1(k1_waybel_5(A,B,C,D,E))) ) )).

fof(cc1_waybel_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m3_pboole(D,A,C,k2_pre_circ(A,B))
         => ( v2_relat_1(D)
            & v1_funcop_1(D) ) ) ) )).

fof(fc2_waybel_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v2_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) )).

fof(fc3_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & l1_orders_2(C)
        & m3_pboole(D,A,B,k2_pre_circ(A,u1_struct_0(C))) )
     => ~ v1_xboole_0(k2_relat_1(k4_waybel_5(C,D))) ) )).

fof(fc4_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & ~ v3_struct_0(C)
        & l1_orders_2(C)
        & m3_pboole(D,A,B,k2_pre_circ(A,u1_struct_0(C))) )
     => ~ v1_xboole_0(k2_relat_1(k5_waybel_5(C,D))) ) )).

fof(cc2_waybel_5,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_waybel_5(A) ) ) ) )).

fof(rc1_waybel_5,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)
      & v1_waybel_5(A) ) )).

fof(cc3_waybel_5,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v1_waybel_5(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)
          & v24_waybel_0(A)
          & v25_waybel_0(A)
          & v2_waybel_3(A)
          & v3_waybel_3(A) ) ) ) )).

fof(cc4_waybel_5,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v1_waybel_5(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v9_waybel_1(A) ) ) ) )).

fof(t1_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( ~ v1_xboole_0(k1_waybel_3(A,B))
              & v1_waybel_0(k1_waybel_3(A,B),A)
              & v12_waybel_0(k1_waybel_3(A,B),A)
              & m1_subset_1(k1_waybel_3(A,B),k1_zfmisc_1(u1_struct_0(A)))
              & r3_orders_2(A,B,k1_yellow_0(A,k1_waybel_3(A,B)))
              & ! [C] :
                  ( ( ~ v1_xboole_0(C)
                    & v1_waybel_0(C,A)
                    & v12_waybel_0(C,A)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( r3_orders_2(A,B,k1_yellow_0(A,C))
                   => r1_tarski(k1_waybel_3(A,B),C) ) ) ) ) ) ) )).

fof(t2_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( ~ v1_xboole_0(C)
                & v1_waybel_0(C,A)
                & v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & r3_orders_2(A,B,k1_yellow_0(A,C))
                & ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & v12_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ( r3_orders_2(A,B,k1_yellow_0(A,D))
                     => r1_tarski(C,D) ) ) ) ) ) ) )).

fof(t3_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) )).

fof(t4_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_yellow_0(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ( v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
       => v3_waybel_3(A) ) ) )).

fof(t5_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ( v17_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
          & v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) )
       => v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) )).

fof(t6_waybel_5,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( m3_pboole(D,A,C,k2_pre_circ(A,B))
         => ! [E] :
              ( r2_hidden(E,A)
             => ( v1_funct_1(k1_funct_1(D,E))
                & v1_funct_2(k1_funct_1(D,E),k1_funct_1(C,E),B)
                & m2_relset_1(k1_funct_1(D,E),k1_funct_1(C,E),B) ) ) ) ) )).

fof(t7_waybel_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) )).

fof(t8_waybel_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
           => ( k1_relat_1(B) = k1_relat_1(A)
              & k1_relat_1(A) = k1_relat_1(k1_funct_1(k3_pralg_2(A),B)) ) ) ) ) )).

fof(t9_waybel_5,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
           => ! [C] :
                ( r2_hidden(C,k1_relat_1(A))
               => ( r2_hidden(k1_funct_1(B,C),k1_relat_1(k1_funct_1(A,C)))
                  & k1_funct_1(k1_funct_1(k3_pralg_2(A),B),C) = k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C))
                  & r2_hidden(k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C)),k2_relat_1(k1_funct_1(k3_pralg_2(A),B))) ) ) ) ) ) )).

fof(t10_waybel_5,axiom,(
    ! [A,B,C] :
      ( m1_pboole(C,A)
     => ! [D] :
          ( m3_pboole(D,A,C,k2_pre_circ(A,B))
         => ! [E] :
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ( r2_hidden(E,k1_relat_1(k3_pralg_2(D)))
               => ( v1_funct_1(k1_funct_1(k3_pralg_2(D),E))
                  & v1_funct_2(k1_funct_1(k3_pralg_2(D),E),A,B)
                  & m2_relset_1(k1_funct_1(k3_pralg_2(D),E),A,B) ) ) ) ) ) )).

fof(d1_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_relat_1(B),u1_struct_0(A))
                & m2_relset_1(C,k1_relat_1(B),u1_struct_0(A)) )
             => ( C = k4_waybel_5(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,k1_relat_1(B))
                   => k1_funct_1(C,D) = k5_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) )).

fof(d2_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k1_relat_1(B),u1_struct_0(A))
                & m2_relset_1(C,k1_relat_1(B),u1_struct_0(A)) )
             => ( C = k5_waybel_5(A,B)
              <=> ! [D] :
                    ( r2_hidden(D,k1_relat_1(B))
                   => k1_funct_1(C,D) = k6_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) )).

fof(t11_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( ( k1_relat_1(B) = k1_relat_1(C)
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(B))
                     => k5_yellow_2(A,k1_funct_1(B,D)) = k5_yellow_2(A,k1_funct_1(C,D)) ) )
               => k4_waybel_5(A,B) = k4_waybel_5(A,C) ) ) ) ) )).

fof(t12_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( ( k1_relat_1(B) = k1_relat_1(C)
                  & ! [D] :
                      ( r2_hidden(D,k1_relat_1(B))
                     => k6_yellow_2(A,k1_funct_1(B,D)) = k6_yellow_2(A,k1_funct_1(C,D)) ) )
               => k5_waybel_5(A,B) = k5_waybel_5(A,C) ) ) ) ) )).

fof(t13_waybel_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_funcop_1(C) )
         => ( ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k4_waybel_5(B,C)))
                & ! [D] :
                    ~ ( r2_hidden(D,k1_relat_1(C))
                      & A = k5_yellow_2(B,k1_funct_1(C,D)) ) )
            & ( ? [D] :
                  ( r2_hidden(D,k1_relat_1(C))
                  & A = k5_yellow_2(B,k1_funct_1(C,D)) )
             => r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k4_waybel_5(B,C))) )
            & ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k5_waybel_5(B,C)))
                & ! [D] :
                    ~ ( r2_hidden(D,k1_relat_1(C))
                      & A = k6_yellow_2(B,k1_funct_1(C,D)) ) )
            & ( ? [D] :
                  ( r2_hidden(D,k1_relat_1(C))
                  & A = k6_yellow_2(B,k1_funct_1(C,D)) )
             => r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k5_waybel_5(B,C))) ) ) ) ) )).

fof(t14_waybel_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( m1_pboole(D,C)
             => ! [E] :
                  ( m3_pboole(E,C,D,k2_pre_circ(C,u1_struct_0(B)))
                 => ( ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k4_waybel_5(B,E)))
                        & ! [F] :
                            ( m1_subset_1(F,C)
                           => A != k5_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) )
                    & ( ? [F] :
                          ( m1_subset_1(F,C)
                          & A = k5_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) )
                     => r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k4_waybel_5(B,E))) )
                    & ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k5_waybel_5(B,E)))
                        & ! [F] :
                            ( m1_subset_1(F,C)
                           => A != k6_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) )
                    & ( ? [F] :
                          ( m1_subset_1(F,C)
                          & A = k6_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) )
                     => r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k5_waybel_5(B,E))) ) ) ) ) ) ) )).

fof(t15_waybel_5,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,u1_struct_0(A))
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( ! [D] :
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ( r2_hidden(D,k1_relat_1(k3_pralg_2(C)))
                     => r3_orders_2(A,k6_yellow_2(A,k1_funct_1(k3_pralg_2(C),D)),B) ) )
               => r3_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,k3_pralg_2(C))),B) ) ) ) ) )).

fof(t16_waybel_5,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)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,B) )
             => ! [D] :
                  ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                 => r1_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))),k6_yellow_2(A,k4_waybel_5(A,D))) ) ) ) ) )).

fof(t17_waybel_5,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,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v3_waybel_3(A)
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_waybel_3(A,D,B)
                       => r3_orders_2(A,D,C) ) ) )
               => r3_orders_2(A,B,C) ) ) ) ) )).

fof(t18_waybel_5,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)
           => ( r2_hidden(B,k2_yellow_6(u1_struct_0(A)))
             => ! [C] :
                  ( ( v2_relat_1(C)
                    & m1_pboole(C,B) )
                 => ( ! [D] :
                        ( m1_subset_1(D,B)
                       => r2_hidden(k1_funct_1(C,D),k2_yellow_6(u1_struct_0(A))) )
                   => ! [D] :
                        ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                       => ( ! [E] :
                              ( m1_subset_1(E,B)
                             => v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
                         => k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) )
       => v3_waybel_3(A) ) ) )).

fof(t19_waybel_5,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) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( ~ v1_xboole_0(B)
           => ! [C] :
                ( ( v2_relat_1(C)
                  & m1_pboole(C,B) )
               => ! [D] :
                    ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                   => ( ! [E] :
                          ( m1_subset_1(E,B)
                         => v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
                     => k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) ) )).

fof(t20_waybel_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ( k1_relat_1(k6_waybel_5(A,B,C,F)) = A
                            & k1_relat_1(k1_waybel_5(A,C,k2_pre_circ(A,B),k6_waybel_5(A,B,C,F),D)) = B
                            & k1_funct_1(F,k4_tarski(D,E)) = k1_funct_1(k1_waybel_5(A,C,k2_pre_circ(A,B),k6_waybel_5(A,B,C,F),D),E) ) ) ) ) ) ) ) )).

fof(t21_waybel_5,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) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( ~ v1_xboole_0(B)
           => ! [C] :
                ( ~ v1_xboole_0(C)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
                      & m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
                   => ( ! [E] :
                          ( m1_subset_1(E,B)
                         => v1_waybel_0(k8_yellow_2(k1_funct_1(k2_pre_circ(B,C),E),A,k1_waybel_5(B,u1_struct_0(A),k2_pre_circ(B,C),k6_waybel_5(B,C,u1_struct_0(A),D),E)),A) )
                     => k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D))) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),k2_pre_circ(B,C),k6_waybel_5(B,C,u1_struct_0(A),D)))) ) ) ) ) ) ) )).

fof(d3_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_waybel_5(A)
      <=> ( v3_lattice3(A)
          & ! [B] :
              ( ~ v1_xboole_0(B)
             => ! [C] :
                  ( ( v2_relat_1(C)
                    & m1_pboole(C,B) )
                 => ! [D] :
                      ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                     => k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) ) )).

fof(t24_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_waybel_5(A)
        & l1_orders_2(A) )
     => v3_waybel_3(A) ) )).

fof(t27_waybel_5,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)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,B) )
             => ! [D] :
                  ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                 => ( ! [E] :
                        ( m1_subset_1(E,B)
                       => v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
                   => v1_waybel_0(k8_yellow_2(k1_relat_1(k2_waybel_5(B,u1_struct_0(A),C,D)),A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))),A) ) ) ) ) ) )).

fof(t28_waybel_5,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) )
     => ( v3_waybel_3(A)
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v4_yellow_0(B,A)
              & v7_yellow_0(B,A)
              & v4_waybel_0(B,A)
              & m1_yellow_0(B,A) )
           => ( v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & v3_waybel_3(B)
              & l1_orders_2(B) ) ) ) ) )).

fof(t29_waybel_5,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)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ( ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & v17_waybel_0(C,A,B)
                & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
           => ( v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & v2_lattice3(B)
              & v3_lattice3(B)
              & l1_orders_2(B) ) ) ) ) )).

fof(t30_waybel_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,C)
            & m2_relset_1(D,B,C) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & v1_funct_2(E,C,B)
                & m2_relset_1(E,C,B) )
             => ( k1_partfun1(B,C,C,B,D,E) = k6_partfun1(B)
               => k13_pboole(k8_waybel_5(B,C,A,D),k8_waybel_5(C,B,A,E)) = k2_msualg_3(A,k2_pre_circ(A,B)) ) ) ) ) )).

fof(t31_waybel_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m3_pboole(E,A,D,k2_pre_circ(A,B))
                 => ! [F] :
                      ( ( v1_funct_1(F)
                        & v1_funct_2(F,B,C)
                        & m2_relset_1(F,B,C) )
                     => m3_pboole(k13_pboole(E,k8_waybel_5(B,C,A,F)),A,D,k2_pre_circ(A,C)) ) ) ) ) ) )).

fof(t32_waybel_5,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_pboole(D,A)
                 => ! [E] :
                      ( m3_pboole(E,A,D,k2_pre_circ(A,B))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,C)
                            & m2_relset_1(F,B,C) )
                         => k2_funct_6(k3_msualg_3(A,D,k2_pre_circ(A,B),k2_pre_circ(A,C),E,k8_waybel_5(B,C,A,F))) = k2_funct_6(E) ) ) ) ) ) ) )).

fof(t33_waybel_5,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) )
     => ( v3_waybel_3(A)
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & l1_orders_2(B) )
           => ( ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                  & v17_waybel_0(C,A,B)
                  & v22_waybel_0(C,A,B)
                  & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_orders_2(B)
                & v3_orders_2(B)
                & v4_orders_2(B)
                & v1_lattice3(B)
                & v2_lattice3(B)
                & v3_waybel_3(B)
                & l1_orders_2(B) ) ) ) ) ) )).

fof(dt_k1_waybel_5,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k1_waybel_5(A,B,C,D,E))
        & v1_funct_2(k1_waybel_5(A,B,C,D,E),k1_funct_1(C,E),B)
        & m2_relset_1(k1_waybel_5(A,B,C,D,E),k1_funct_1(C,E),B) ) ) )).

fof(redefinition_k1_waybel_5,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m1_subset_1(E,A) )
     => k1_waybel_5(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k2_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B)) )
     => m3_pboole(k2_waybel_5(A,B,C,D),k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B)) ) )).

fof(redefinition_k2_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B)) )
     => k2_waybel_5(A,B,C,D) = k7_funct_6(D) ) )).

fof(dt_k3_waybel_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m3_pboole(E,k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B))
        & m1_subset_1(F,k4_card_3(k2_funct_6(D))) )
     => ( v1_funct_1(k3_waybel_5(A,B,C,D,E,F))
        & v1_funct_2(k3_waybel_5(A,B,C,D,E,F),A,B)
        & m2_relset_1(k3_waybel_5(A,B,C,D,E,F),A,B) ) ) )).

fof(redefinition_k3_waybel_5,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m3_pboole(E,k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B))
        & m1_subset_1(F,k4_card_3(k2_funct_6(D))) )
     => k3_waybel_5(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).

fof(dt_k4_waybel_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B) )
     => ( v1_funct_1(k4_waybel_5(A,B))
        & v1_funct_2(k4_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A))
        & m2_relset_1(k4_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A)) ) ) )).

fof(dt_k5_waybel_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B) )
     => ( v1_funct_1(k5_waybel_5(A,B))
        & v1_funct_2(k5_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A))
        & m2_relset_1(k5_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A)) ) ) )).

fof(dt_k6_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => m3_pboole(k6_waybel_5(A,B,C,D),A,k2_pre_circ(A,B),k2_pre_circ(A,C)) ) )).

fof(redefinition_k6_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k6_waybel_5(A,B,C,D) = k3_funct_5(D) ) )).

fof(dt_k7_waybel_5,axiom,(
    ! [A,B] : m1_pboole(k7_waybel_5(A,B),A) )).

fof(redefinition_k7_waybel_5,axiom,(
    ! [A,B] : k7_waybel_5(A,B) = k2_funcop_1(A,B) )).

fof(dt_k8_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => m3_pboole(k8_waybel_5(A,B,C,D),C,k2_pre_circ(C,A),k2_pre_circ(C,B)) ) )).

fof(redefinition_k8_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => k8_waybel_5(A,B,C,D) = k2_funcop_1(C,D) ) )).

fof(t22_waybel_5,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)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
                    & m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( E = a_4_0_waybel_5(A,B,C,D)
                       => r1_orders_2(A,k1_yellow_0(A,E),k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D)))) ) ) ) ) ) ) )).

fof(t23_waybel_5,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) )
     => ( v3_waybel_3(A)
      <=> ! [B] :
            ( ~ v1_xboole_0(B)
           => ! [C] :
                ( ~ v1_xboole_0(C)
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
                      & m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
                   => ! [E] :
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( E = a_4_0_waybel_5(A,B,C,D)
                         => k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D))) = k1_yellow_0(A,E) ) ) ) ) ) ) ) )).

fof(t25_waybel_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r1_yellow_0(A,C)
                      & r1_yellow_0(A,D)
                      & D = a_3_0_waybel_5(A,B,C) )
                   => r1_orders_2(A,k1_yellow_0(A,D),k12_lattice3(A,B,k1_yellow_0(A,C))) ) ) ) ) ) )).

fof(t26_waybel_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v1_waybel_5(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_1_waybel_5(A,B,C)) ) ) ) )).

fof(fraenkel_a_4_0_waybel_5,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v3_lattice3(B)
        & l1_orders_2(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(C,D),u1_struct_0(B))
        & m2_relset_1(E,k2_zfmisc_1(C,D),u1_struct_0(B)) )
     => ( r2_hidden(A,a_4_0_waybel_5(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,u1_struct_0(B))
            & A = F
            & ? [G] :
                ( v2_relat_1(G)
                & m1_pboole(G,C)
                & r2_hidden(G,k1_funct_2(C,k5_finsub_1(D)))
                & ? [H] :
                    ( m3_pboole(H,C,G,k2_pre_circ(C,u1_struct_0(B)))
                    & ! [I] :
                        ( m1_subset_1(I,C)
                       => ! [J] :
                            ( r2_hidden(J,k1_funct_1(G,I))
                           => k1_funct_1(k1_waybel_5(C,u1_struct_0(B),G,H,I),J) = k1_funct_1(E,k4_tarski(I,J)) ) )
                    & F = k6_yellow_2(B,k4_waybel_5(B,H)) ) ) ) ) ) )).

fof(fraenkel_a_3_0_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v2_lattice3(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_waybel_5(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k12_lattice3(B,C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_3_1_waybel_5,axiom,(
    ! [A,B,C,D] :
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & v1_waybel_5(B)
        & l1_orders_2(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_1_waybel_5(B,C,D))
      <=> ? [E] :
            ( m1_subset_1(E,u1_struct_0(B))
            & A = k12_lattice3(B,D,E)
            & r2_hidden(E,C) ) ) ) )).
%------------------------------------------------------------------------------