SET007 Axioms: SET007+630.ax


%------------------------------------------------------------------------------
% File     : SET007+630 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Function Spaces in the Category of Directed Suprema Preserving Maps
% 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    : waybel27 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   73 (   2 unit)
%            Number of atoms       :  988 (  36 equality)
%            Maximal formula depth :   29 (  11 average)
%            Number of connectives : 1021 ( 106 ~  ;   0  |; 691  &)
%                                         (   8 <=>; 216 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   51 (   0 propositional; 1-3 arity)
%            Number of functors    :   47 (   4 constant; 0-6 arity)
%            Number of variables   :  255 (   0 singleton; 246 !;   9 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_xboole_0(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_waybel27(A)
        & v2_waybel27(A)
        & v3_waybel27(A) ) ) )).

fof(rc1_waybel27,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_waybel27(A)
      & v2_waybel27(A)
      & v3_waybel27(A) ) )).

fof(fc1_waybel27,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_waybel27(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v1_waybel27(k7_relat_1(A,B)) ) ) )).

fof(fc2_waybel27,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_waybel27(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B))
        & v2_waybel27(k7_relat_1(A,B)) ) ) )).

fof(rc2_waybel27,axiom,(
    ! [A,B,C] :
    ? [D] :
      ( m1_pboole(D,k1_funct_2(A,k1_funct_2(B,C)))
      & v1_relat_1(D)
      & v1_funct_1(D)
      & v1_waybel27(D) ) )).

fof(rc3_waybel27,axiom,(
    ! [A,B,C] :
    ? [D] :
      ( m1_pboole(D,k1_funct_2(k2_zfmisc_1(A,B),C))
      & v1_relat_1(D)
      & v1_funct_1(D)
      & v2_waybel27(D) ) )).

fof(cc2_waybel27,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v1_funcop_1(C)
              & v1_partfun1(C,A,B) ) ) ) ) )).

fof(fc3_waybel27,axiom,(
    ! [A] :
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => v1_fraenkel(u1_struct_0(A)) ) )).

fof(fc4_waybel27,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))
        & v1_monoid_0(k6_yellow_1(A,B)) ) ) )).

fof(rc4_waybel27,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & ~ v1_yellow_3(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_monoid_0(A) ) )).

fof(rc5_waybel27,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & ~ v3_struct_0(A)
      & v1_monoid_0(A) ) )).

fof(cc3_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_monoid_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_yellow_0(B,A)
         => ( ~ v3_struct_0(B)
           => ( ~ v3_struct_0(B)
              & v1_monoid_0(B) ) ) ) ) )).

fof(fc5_waybel27,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k2_waybel27(A,B))
        & v1_orders_2(k2_waybel27(A,B))
        & v2_orders_2(k2_waybel27(A,B))
        & v4_orders_2(k2_waybel27(A,B))
        & ~ v1_yellow_3(k2_waybel27(A,B))
        & v1_monoid_0(k2_waybel27(A,B)) ) ) )).

fof(fc6_waybel27,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k2_waybel27(A,B))
        & v1_orders_2(k2_waybel27(A,B))
        & v2_orders_2(k2_waybel27(A,B))
        & v3_orders_2(k2_waybel27(A,B))
        & v4_orders_2(k2_waybel27(A,B))
        & ~ v1_yellow_3(k2_waybel27(A,B))
        & v1_monoid_0(k2_waybel27(A,B)) ) ) )).

fof(fc7_waybel27,axiom,(
    ! [A,B] :
      ( ( 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)
        & 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) )
     => ( ~ v3_struct_0(k2_waybel27(A,B))
        & v1_orders_2(k2_waybel27(A,B))
        & v2_orders_2(k2_waybel27(A,B))
        & v3_orders_2(k2_waybel27(A,B))
        & v4_orders_2(k2_waybel27(A,B))
        & v1_yellow_0(k2_waybel27(A,B))
        & v2_yellow_0(k2_waybel27(A,B))
        & v3_yellow_0(k2_waybel27(A,B))
        & v24_waybel_0(k2_waybel27(A,B))
        & v25_waybel_0(k2_waybel27(A,B))
        & ~ v1_yellow_3(k2_waybel27(A,B))
        & v1_lattice3(k2_waybel27(A,B))
        & v2_lattice3(k2_waybel27(A,B))
        & v3_lattice3(k2_waybel27(A,B))
        & v1_monoid_0(k2_waybel27(A,B)) ) ) )).

fof(d1_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_waybel27(A)
      <=> ( ! [B] :
              ( r2_hidden(B,k1_relat_1(A))
             => ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_funcop_1(B) ) )
          & ! [B] :
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( r2_hidden(B,k1_relat_1(A))
               => k1_funct_1(A,B) = k4_funct_5(B) ) ) ) ) ) )).

fof(d2_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_waybel27(A)
      <=> ( ! [B] :
              ( r2_hidden(B,k1_relat_1(A))
             => ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_relat_1(k1_funct_5(B)) ) )
          & ! [B] :
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( r2_hidden(B,k1_relat_1(A))
               => k1_funct_1(A,B) = k3_funct_5(B) ) ) ) ) ) )).

fof(d3_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v3_waybel27(A)
      <=> ( ! [B] :
              ( r2_hidden(B,k1_relat_1(A))
             => ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_funcop_1(B) ) )
          & ! [B] :
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( r2_hidden(B,k1_relat_1(A))
               => k1_funct_1(A,B) = k10_funct_6(B) ) ) ) ) ) )).

fof(t1_waybel27,axiom,(
    ! [A,B,C,D] :
      ~ ( r1_tarski(D,k1_funct_2(A,k1_funct_2(B,C)))
        & ! [E] :
            ( m1_pboole(E,D)
           => ~ ( v1_waybel27(E)
                & r1_tarski(k2_relat_1(E),k1_funct_2(k2_zfmisc_1(A,B),C)) ) ) ) )).

fof(t2_waybel27,axiom,(
    ! [A,B,C,D] :
      ~ ( r1_tarski(D,k1_funct_2(k2_zfmisc_1(A,B),C))
        & ! [E] :
            ( m1_pboole(E,D)
           => ~ ( v2_waybel27(E)
                & ( ( B = k1_xboole_0
                   => A = k1_xboole_0 )
                 => r1_tarski(k2_relat_1(E),k1_funct_2(A,k1_funct_2(B,C))) ) ) ) ) )).

fof(t3_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v3_waybel27(D) )
             => ! [E] :
                  ( ( v1_relat_1(E)
                    & v1_funct_1(E)
                    & v3_waybel27(E) )
                 => ( ( r1_tarski(k1_relat_1(D),k1_funct_2(A,k1_funct_2(B,C)))
                      & r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
                   => k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) ) ) )).

fof(t4_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_waybel27(D) )
         => ! [E] :
              ( ( v1_relat_1(E)
                & v1_funct_1(E)
                & v2_waybel27(E) )
             => ( ( r1_tarski(k1_relat_1(D),k1_funct_2(B,k1_funct_2(A,C)))
                  & r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
               => k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) ) )).

fof(t5_waybel27,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D)
        & v2_waybel27(D) )
     => ! [E] :
          ( ( v1_relat_1(E)
            & v1_funct_1(E)
            & v1_waybel27(E) )
         => ( ( r1_tarski(k1_relat_1(D),k1_funct_2(k2_zfmisc_1(A,B),C))
              & r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
           => k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) )).

fof(t6_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B,C] :
          ( r2_hidden(B,k1_relat_1(k10_funct_6(A)))
         => r1_tarski(k9_relat_1(k1_funct_1(k10_funct_6(A),B),C),k5_card_3(B,k9_relat_1(A,C))) ) ) )).

fof(t7_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B,C] :
          ( ! [D] :
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( r2_hidden(D,k9_relat_1(A,C))
               => r2_hidden(B,k1_relat_1(D)) ) )
         => r1_tarski(k5_card_3(B,k9_relat_1(A,C)),k9_relat_1(k1_funct_1(k10_funct_6(A),B),C)) ) ) )).

fof(t8_waybel27,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
       => ! [D,E] :
            ( r2_hidden(D,A)
           => k9_relat_1(k1_funct_1(k10_funct_6(C),D),E) = k5_card_3(D,k9_relat_1(C,E)) ) ) ) )).

fof(t9_waybel27,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] :
          ( r1_tarski(k2_zfmisc_1(C,k1_tarski(B)),k1_relat_1(A))
         => k5_card_3(B,k9_relat_1(k3_funct_5(A),C)) = k9_relat_1(A,k2_zfmisc_1(C,k1_tarski(B))) ) ) )).

fof(t10_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & v11_quantal1(C)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C))) )
                 => k1_partfun1(u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C)),u1_struct_0(B),u1_struct_0(B),D,C) = D ) ) ) ) )).

fof(t11_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ( m1_yellow_0(B,C)
               => ! [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)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                       => ( ( v5_orders_3(D,A,B)
                            & D = E )
                         => v5_orders_3(E,A,C) ) ) ) ) ) ) ) )).

fof(t12_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ( ( v4_yellow_0(B,C)
                  & m1_yellow_0(B,C) )
               => ! [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)) )
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
                       => ( ( v5_orders_3(E,A,C)
                            & D = E )
                         => v5_orders_3(D,A,B) ) ) ) ) ) ) ) )).

fof(t13_waybel27,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ( k3_funct_2(A,k2_tarski(np__0,np__1),k5_funct_3(B,A),k1_tarski(np__1)) = B
        & k3_funct_2(A,k2_tarski(np__0,np__1),k5_funct_3(B,A),k1_tarski(np__0)) = k4_xboole_0(A,B) ) ) )).

fof(t14_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k6_yellow_1(A,B)))
                 => ( r1_orders_2(k6_yellow_1(A,B),C,D)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => r1_orders_2(B,k1_waybel27(A,B,C,E),k1_waybel27(A,B,D,E)) ) ) ) ) ) ) )).

fof(t15_waybel27,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_orders_2(B) )
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & l1_orders_2(C) )
         => ( g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
           => k6_yellow_1(A,B) = k6_yellow_1(A,C) ) ) ) )).

fof(t16_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_pre_topc(D)
                    & l1_pre_topc(D) )
                 => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) )
                   => k1_waybel26(A,C) = k1_waybel26(B,D) ) ) ) ) ) )).

fof(t17_waybel27,axiom,(
    ! [A] :
    ? [B] :
      ( v1_funct_1(B)
      & v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(np__1))))
      & m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(np__1))))
      & v23_waybel_0(B,k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(np__1)))
      & ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) )).

fof(t18_waybel27,axiom,(
    ! [A] : r5_waybel_1(k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(np__1))) )).

fof(t19_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,k6_yellow_1(B,k6_yellow_1(A,C)))
                    & m1_yellow_0(D,k6_yellow_1(B,k6_yellow_1(A,C))) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v4_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C)))
                        & m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
                            & m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
                         => ( v3_waybel27(F)
                           => v5_orders_3(F,D,E) ) ) ) ) ) ) ) )).

fof(t20_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C)))
                    & m1_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C))) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v4_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C))
                        & m1_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
                            & m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
                         => ( v1_waybel27(F)
                           => v5_orders_3(F,D,E) ) ) ) ) ) ) ) )).

fof(t21_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C)))
                    & m1_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C))) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v4_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C))
                        & m1_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(E),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(E),u1_struct_0(D)) )
                         => ( v2_waybel27(F)
                           => v5_orders_3(F,E,D) ) ) ) ) ) ) ) )).

fof(d4_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_orders_2(C)
                & l1_orders_2(C) )
             => ( C = k2_waybel27(A,B)
              <=> ( v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
                  & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
                  & ! [D] :
                      ( r2_hidden(D,u1_struct_0(C))
                    <=> ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                        & v22_waybel_0(D,A,B)
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) ) )).

fof(t22_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => r1_tarski(u1_struct_0(k2_waybel27(A,B)),k1_funct_2(u1_struct_0(A),u1_struct_0(B))) ) ) )).

fof(t23_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k2_waybel27(A,B)))
                 => ( r3_orders_2(k2_waybel27(A,B),C,D)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r3_orders_2(B,k3_waybel27(A,B,C,E),k3_waybel27(A,B,D,E)) ) ) ) ) ) ) )).

fof(t24_waybel27,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v4_waybel11(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_pre_topc(B)
            & v4_waybel11(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_waybel_9(B) )
         => k2_waybel27(A,B) = k2_waybel17(A,B) ) ) )).

fof(t25_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_orders_2(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
                      & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
                   => k2_waybel27(A,C) = k2_waybel27(B,D) ) ) ) ) ) )).

fof(t26_waybel27,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] :
          ( ( 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) )
         => ( v8_yellow_0(k2_waybel27(A,B),k6_yellow_1(u1_struct_0(A),B))
            & m1_yellow_0(k2_waybel27(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ) )).

fof(t27_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_waybel27(A,B))))
             => k1_yellow_0(k2_waybel27(A,B),C) = k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C) ) ) ) )).

fof(d5_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_orders_2(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ( v22_waybel_0(E,A,B)
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                              & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                           => ( v22_waybel_0(F,C,D)
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D)))
                                    & m2_relset_1(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) )
                                 => ( G = k4_waybel27(A,B,C,D,E,F)
                                  <=> ! [H] :
                                        ( ( v1_funct_1(H)
                                          & v1_funct_2(H,u1_struct_0(B),u1_struct_0(C))
                                          & v22_waybel_0(H,B,C)
                                          & m2_relset_1(H,u1_struct_0(B),u1_struct_0(C)) )
                                       => k1_funct_1(G,H) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(D),E,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),H,F)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(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] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v2_orders_2(D)
                    & v3_orders_2(D)
                    & v4_orders_2(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v2_orders_2(E)
                        & v3_orders_2(E)
                        & v4_orders_2(E)
                        & l1_orders_2(E) )
                     => ! [F] :
                          ( ( ~ v3_struct_0(F)
                            & v2_orders_2(F)
                            & v3_orders_2(F)
                            & v4_orders_2(F)
                            & l1_orders_2(F) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
                                & v22_waybel_0(G,B,C)
                                & m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,u1_struct_0(A),u1_struct_0(B))
                                    & v22_waybel_0(H,A,B)
                                    & m2_relset_1(H,u1_struct_0(A),u1_struct_0(B)) )
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(D),u1_struct_0(E))
                                        & v22_waybel_0(I,D,E)
                                        & m2_relset_1(I,u1_struct_0(D),u1_struct_0(E)) )
                                     => ! [J] :
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,u1_struct_0(E),u1_struct_0(F))
                                            & v22_waybel_0(J,E,F)
                                            & m2_relset_1(J,u1_struct_0(E),u1_struct_0(F)) )
                                         => k7_funct_2(u1_struct_0(k2_waybel27(C,D)),u1_struct_0(k2_waybel27(B,E)),u1_struct_0(k2_waybel27(A,F)),k4_waybel27(B,C,D,E,G,I),k4_waybel27(A,B,E,F,H,J)) = k4_waybel27(A,C,D,F,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),H,G),k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),I,J)) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_waybel27,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => k4_waybel27(A,A,B,B,k7_grcat_1(A),k7_grcat_1(B)) = k7_grcat_1(k2_waybel27(A,B)) ) ) )).

fof(t30_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v2_orders_2(D)
                    & v3_orders_2(D)
                    & v4_orders_2(D)
                    & v1_lattice3(D)
                    & v2_lattice3(D)
                    & v3_lattice3(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & v22_waybel_0(E,A,B)
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & v22_waybel_0(F,C,D)
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => v22_waybel_0(k4_waybel27(A,B,C,D,E,F),k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ) )).

fof(t31_waybel27,axiom,(
    v4_waybel11(k1_waybel25(k9_waybel18)) )).

fof(t32_waybel27,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_pre_topc(A)
        & v4_waybel11(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_waybel_9(A) )
     => k1_waybel26(A,k9_waybel18) = k2_waybel27(A,k3_yellow_1(np__1)) ) )).

fof(t33_waybel27,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_funct_1(B)
          & v1_funct_2(B,u1_struct_0(k2_waybel27(A,k3_yellow_1(np__1))),u1_struct_0(k2_yellow_1(k5_waybel11(A))))
          & m2_relset_1(B,u1_struct_0(k2_waybel27(A,k3_yellow_1(np__1))),u1_struct_0(k2_yellow_1(k5_waybel11(A))))
          & v23_waybel_0(B,k2_waybel27(A,k3_yellow_1(np__1)),k2_yellow_1(k5_waybel11(A)))
          & ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_yellow_1(np__1)))
                & v22_waybel_0(C,A,k3_yellow_1(np__1))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_yellow_1(np__1))) )
             => k1_funct_1(B,C) = k5_pre_topc(A,k3_yellow_1(np__1),C,k1_tarski(np__1)) ) ) ) )).

fof(t34_waybel27,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) )
     => r5_waybel_1(k2_waybel27(A,k3_yellow_1(np__1)),k2_yellow_1(k5_waybel11(A))) ) )).

fof(t35_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v2_orders_2(D)
                    & v3_orders_2(D)
                    & v4_orders_2(D)
                    & v1_lattice3(D)
                    & v2_lattice3(D)
                    & v3_lattice3(D)
                    & l1_orders_2(D) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                         => ( ( v23_waybel_0(E,A,B)
                              & v23_waybel_0(F,C,D) )
                           => v23_waybel_0(k4_waybel27(A,B,C,D,E,F),k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ) ) )).

fof(t36_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v2_orders_2(D)
                    & v3_orders_2(D)
                    & v4_orders_2(D)
                    & v1_lattice3(D)
                    & v2_lattice3(D)
                    & v3_lattice3(D)
                    & l1_orders_2(D) )
                 => ( ( r5_waybel_1(A,B)
                      & r5_waybel_1(C,D) )
                   => r5_waybel_1(k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) )).

fof(t37_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
                & v22_waybel_0(C,B,B)
                & v6_waybel_1(C,B)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
             => k2_yellow_2(k2_waybel27(A,B),k2_waybel27(A,B),k4_waybel27(A,A,B,B,k7_grcat_1(A),C)) = k2_waybel27(A,k2_yellow_2(B,B,C)) ) ) ) )).

fof(t38_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
                    & v22_waybel_0(D,B,k6_yellow_1(A,C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) )
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ( v1_funct_1(k1_funct_1(k10_funct_6(D),E))
                        & v1_funct_2(k1_funct_1(k10_funct_6(D),E),u1_struct_0(B),u1_struct_0(C))
                        & v22_waybel_0(k1_funct_1(k10_funct_6(D),E),B,C)
                        & m2_relset_1(k1_funct_1(k10_funct_6(D),E),u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) )).

fof(t39_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
                    & v22_waybel_0(D,B,k6_yellow_1(A,C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) )
                 => ( v1_funct_1(k10_funct_6(D))
                    & v1_funct_2(k10_funct_6(D),A,u1_struct_0(k2_waybel27(B,C)))
                    & m2_relset_1(k10_funct_6(D),A,u1_struct_0(k2_waybel27(B,C))) ) ) ) ) ) )).

fof(t40_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,u1_struct_0(k2_waybel27(B,C)))
                    & m2_relset_1(D,A,u1_struct_0(k2_waybel27(B,C))) )
                 => ( v1_funct_1(k10_funct_6(D))
                    & v1_funct_2(k10_funct_6(D),u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
                    & v22_waybel_0(k10_funct_6(D),B,k6_yellow_1(A,C))
                    & m2_relset_1(k10_funct_6(D),u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) ) ) ) ) ) )).

fof(t41_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(k2_waybel27(B,k6_yellow_1(A,C))),u1_struct_0(k6_yellow_1(A,k2_waybel27(B,C))))
                  & m2_relset_1(D,u1_struct_0(k2_waybel27(B,k6_yellow_1(A,C))),u1_struct_0(k6_yellow_1(A,k2_waybel27(B,C))))
                  & v3_waybel27(D)
                  & v23_waybel_0(D,k2_waybel27(B,k6_yellow_1(A,C)),k6_yellow_1(A,k2_waybel27(B,C))) ) ) ) ) )).

fof(t42_waybel27,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & l1_orders_2(C) )
             => r5_waybel_1(k2_waybel27(B,k6_yellow_1(A,C)),k6_yellow_1(A,k2_waybel27(B,C))) ) ) ) )).

fof(t43_waybel27,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & v3_waybel_3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & v3_waybel_3(B)
            & l1_orders_2(B) )
         => v3_waybel_3(k2_waybel27(A,B)) ) ) )).

fof(t44_waybel27,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_waybel_8(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v2_waybel_8(B)
            & v1_lattice3(B)
            & v2_lattice3(B)
            & v3_lattice3(B)
            & l1_orders_2(B) )
         => v2_waybel_8(k2_waybel27(A,B)) ) ) )).

fof(t45_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_waybel27(B,C)))
                    & v22_waybel_0(D,A,k2_waybel27(B,C))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_waybel27(B,C))) )
                 => ( v1_funct_1(k4_funct_5(D))
                    & v1_funct_2(k4_funct_5(D),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
                    & v22_waybel_0(k4_funct_5(D),k3_yellow_3(A,B),C)
                    & m2_relset_1(k4_funct_5(D),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) ) ) ) ) ) )).

fof(t46_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
                    & v22_waybel_0(D,k3_yellow_3(A,B),C)
                    & m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
                 => ( v1_funct_1(k3_funct_5(D))
                    & v1_funct_2(k3_funct_5(D),u1_struct_0(A),u1_struct_0(k2_waybel27(B,C)))
                    & v22_waybel_0(k3_funct_5(D),A,k2_waybel27(B,C))
                    & m2_relset_1(k3_funct_5(D),u1_struct_0(A),u1_struct_0(k2_waybel27(B,C))) ) ) ) ) ) )).

fof(t47_waybel27,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] :
          ( ( 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) )
         => ! [C] :
              ( ( v2_orders_2(C)
                & v3_orders_2(C)
                & v4_orders_2(C)
                & v1_lattice3(C)
                & v2_lattice3(C)
                & v3_lattice3(C)
                & l1_orders_2(C) )
             => ? [D] :
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(k2_waybel27(A,k2_waybel27(B,C))),u1_struct_0(k2_waybel27(k3_yellow_3(A,B),C)))
                  & m2_relset_1(D,u1_struct_0(k2_waybel27(A,k2_waybel27(B,C))),u1_struct_0(k2_waybel27(k3_yellow_3(A,B),C)))
                  & v1_waybel27(D)
                  & v23_waybel_0(D,k2_waybel27(A,k2_waybel27(B,C)),k2_waybel27(k3_yellow_3(A,B),C)) ) ) ) ) )).

fof(dt_k1_waybel27,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
        & m1_subset_1(D,A) )
     => m1_subset_1(k1_waybel27(A,B,C,D),u1_struct_0(B)) ) )).

fof(redefinition_k1_waybel27,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
        & m1_subset_1(D,A) )
     => k1_waybel27(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k2_waybel27,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( v1_orders_2(k2_waybel27(A,B))
        & l1_orders_2(k2_waybel27(A,B)) ) ) )).

fof(dt_k3_waybel27,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k3_waybel27(A,B,C,D),u1_struct_0(B)) ) )).

fof(redefinition_k3_waybel27,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
        & m1_subset_1(D,u1_struct_0(A)) )
     => k3_waybel27(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k4_waybel27,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & ~ v3_struct_0(B)
        & v2_orders_2(B)
        & v4_orders_2(B)
        & l1_orders_2(B)
        & ~ v3_struct_0(C)
        & v2_orders_2(C)
        & v4_orders_2(C)
        & l1_orders_2(C)
        & ~ v3_struct_0(D)
        & v2_orders_2(D)
        & v4_orders_2(D)
        & l1_orders_2(D)
        & v1_funct_1(E)
        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(E,u1_struct_0(A),u1_struct_0(B))
        & v1_funct_1(F)
        & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
        & m1_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
     => ( v1_funct_1(k4_waybel27(A,B,C,D,E,F))
        & v1_funct_2(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D)))
        & m2_relset_1(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) ) ) )).
%------------------------------------------------------------------------------