SET007 Axioms: SET007+545.ax


%------------------------------------------------------------------------------
% File     : SET007+545 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Injective Spaces
% 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    : waybel18 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (   0 unit)
%            Number of atoms       :  430 (  35 equality)
%            Maximal formula depth :   21 (   8 average)
%            Number of connectives :  439 (  68 ~  ;   1  |; 258  &)
%                                         (  11 <=>; 101 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   54 (   0 propositional; 1-3 arity)
%            Number of functors    :   41 (   4 constant; 0-5 arity)
%            Number of variables   :  148 (   0 singleton; 138 !;  10 ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_waybel18,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_waybel18(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) )).

fof(rc1_waybel18,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_waybel18(B) ) )).

fof(rc2_waybel18,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v4_waybel_3(B)
      & v2_pralg_1(B)
      & v1_waybel18(B) ) )).

fof(fc1_waybel18,axiom,(
    ! [A,B] :
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k3_waybel18(A,B))
        & v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B)) ) ) )).

fof(fc2_waybel18,axiom,(
    ! [A,B] :
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k3_waybel18(A,B))
        & v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B))
        & v1_monoid_0(k3_waybel18(A,B)) ) ) )).

fof(fc3_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ~ v3_struct_0(k7_waybel18(A,B,C)) ) )).

fof(fc4_waybel18,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_relat_1(k8_waybel18(A,B,C))
        & v1_funct_1(k8_waybel18(A,B,C))
        & v1_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C)))
        & v2_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C))) ) ) )).

fof(fc5_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18) )).

fof(fc6_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18)
    & v2_t_0topsp(k9_waybel18) )).

fof(fc7_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18)
    & v2_t_0topsp(k9_waybel18)
    & v2_waybel18(k9_waybel18) )).

fof(fc8_waybel18,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v4_waybel_3(k2_funcop_1(A,B)) ) ) )).

fof(fc9_waybel18,axiom,(
    ! [A,B] :
      ( l1_pre_topc(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B))
        & v1_waybel18(k2_funcop_1(A,B)) ) ) )).

fof(fc10_waybel18,axiom,(
    ! [A,B] :
      ( ( v2_orders_2(B)
        & l1_orders_2(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_yellow_1(k2_funcop_1(A,B))
        & v5_waybel_3(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B)) ) ) )).

fof(fc11_waybel18,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v4_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) )).

fof(fc12_waybel18,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_orders_2(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) )).

fof(fc13_waybel18,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(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(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) )).

fof(fc14_waybel18,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_yellow_0(B)
        & v2_waybel_8(B)
        & v1_lattice3(B)
        & v2_lattice3(B)
        & l1_orders_2(B) )
     => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) )).

fof(t1_waybel18,axiom,(
    ! [A,B,C,D] :
      ( r1_tarski(D,k1_enumset1(A,B,C))
    <=> ~ ( D != k1_xboole_0
          & D != k1_tarski(A)
          & D != k1_tarski(B)
          & D != k1_tarski(C)
          & D != k2_tarski(A,B)
          & D != k2_tarski(B,C)
          & D != k2_tarski(A,C)
          & D != k1_enumset1(A,B,C) ) ) )).

fof(t2_waybel18,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( ( C = k4_xboole_0(B,k1_tarski(k1_xboole_0))
              | B = k2_xboole_0(C,k1_tarski(k1_xboole_0)) )
           => k1_cantor_1(A,B) = k1_cantor_1(A,C) ) ) ) )).

fof(t3_waybel18,axiom,(
    ! [A] :
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( m1_cantor_1(B,A)
          <=> m1_cantor_1(k4_xboole_0(B,k1_tarski(k1_xboole_0)),A) ) ) ) )).

fof(d1_waybel18,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_waybel18(A)
      <=> ! [B] :
            ( r2_hidden(B,k2_relat_1(A))
           => l1_pre_topc(B) ) ) ) )).

fof(d2_waybel18,axiom,(
    ! [A,B] :
      ( ( v1_waybel18(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B)))))
         => ( C = k2_waybel18(A,B)
          <=> ! [D] :
                ( m1_subset_1(D,k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))
               => ( r2_hidden(D,C)
                <=> ? [E,F] :
                      ( l1_pre_topc(F)
                      & ? [G] :
                          ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(F)))
                          & r2_hidden(E,A)
                          & v3_pre_topc(G,F)
                          & F = k1_funct_1(B,E)
                          & D = k4_card_3(k2_funct_7(k12_pralg_1(A,B),E,G)) ) ) ) ) ) ) ) )).

fof(t4_waybel18,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => v2_pre_topc(g1_pre_topc(A,k1_cantor_1(A,k2_cantor_1(A,B)))) ) )).

fof(d3_waybel18,axiom,(
    ! [A,B] :
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v1_pre_topc(C)
            & v2_pre_topc(C)
            & l1_pre_topc(C) )
         => ( C = k3_waybel18(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) )).

fof(d4_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => k6_waybel18(A,B,C) = k3_pralg_3(k12_pralg_1(A,B),C) ) ) ) )).

fof(t5_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))
                 => k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),D) = k4_card_3(k2_funct_7(k12_pralg_1(A,B),C,D)) ) ) ) ) )).

fof(t6_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_subset_1(C,A)
             => v5_pre_topc(k6_waybel18(A,B,C),k3_waybel18(A,B),k4_waybel18(A,B,C)) ) ) ) )).

fof(t7_waybel18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v4_waybel_3(C)
                & v1_waybel18(C)
                & m1_pboole(C,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,C)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k3_waybel18(B,C))) )
                 => ( v5_pre_topc(D,A,k3_waybel18(B,C))
                  <=> ! [E] :
                        ( m1_subset_1(E,B)
                       => v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(k3_waybel18(B,C)),u1_struct_0(k4_waybel18(B,C,E)),D,k6_waybel18(B,C,E)),A,k4_waybel18(B,C,E)) ) ) ) ) ) ) )).

fof(d5_waybel18,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v2_waybel18(A)
      <=> ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_pre_topc(B)
              & l1_pre_topc(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)) )
               => ( v5_pre_topc(C,B,A)
                 => ! [D] :
                      ( ( ~ v3_struct_0(D)
                        & v2_pre_topc(D)
                        & l1_pre_topc(D) )
                     => ~ ( m1_pre_topc(B,D)
                          & ! [E] :
                              ( ( v1_funct_1(E)
                                & v1_funct_2(E,u1_struct_0(D),u1_struct_0(A))
                                & m2_relset_1(E,u1_struct_0(D),u1_struct_0(A)) )
                             => ~ ( v5_pre_topc(E,D,A)
                                  & k7_relat_1(E,u1_struct_0(B)) = C ) ) ) ) ) ) ) ) ) )).

fof(t8_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => v2_waybel18(k4_waybel18(A,B,C)) )
           => v2_waybel18(k3_waybel18(A,B)) ) ) ) )).

fof(t9_waybel18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v2_waybel18(A)
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & m1_pre_topc(B,A) )
           => ( r1_borsuk_1(A,B)
             => v2_waybel18(B) ) ) ) ) )).

fof(d6_waybel18,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_pre_topc(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)) )
             => k7_waybel18(A,B,C) = k3_pre_topc(B,k1_yellow_2(A,B,C)) ) ) ) )).

fof(t10_waybel18,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_pre_topc(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)) )
             => u1_struct_0(k7_waybel18(A,B,C)) = k1_yellow_2(A,B,C) ) ) ) )).

fof(d7_waybel18,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(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)) )
             => k8_waybel18(A,B,C) = C ) ) ) )).

fof(t11_waybel18,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] :
              ( ( 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)) )
             => ( v5_pre_topc(C,A,B)
               => v5_pre_topc(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C)) ) ) ) ) )).

fof(d8_waybel18,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( r1_waybel18(A,B)
          <=> ? [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))
                & v5_pre_topc(C,B,B)
                & k2_monoid_0(u1_struct_0(B),C,C) = C
                & r1_t_0topsp(k7_waybel18(B,B,C),A) ) ) ) ) )).

fof(t12_waybel18,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) )
         => ( v2_waybel18(A)
           => ! [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)) )
               => ( v3_tops_2(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C))
                 => r1_waybel18(A,B) ) ) ) ) ) )).

fof(d9_waybel18,axiom,(
    ! [A] :
      ( ( v1_pre_topc(A)
        & l1_pre_topc(A) )
     => ( A = k9_waybel18
      <=> ( u1_struct_0(A) = k2_tarski(np__0,np__1)
          & u1_pre_topc(A) = k1_enumset1(k1_xboole_0,k1_tarski(np__1),k2_tarski(np__0,np__1)) ) ) ) )).

fof(t13_waybel18,axiom,(
    ! [A] :
      ( ( v4_waybel11(A)
        & m1_yellow_9(A,k3_yellow_1(np__1)) )
     => u1_pre_topc(A) = u1_pre_topc(k9_waybel18) ) )).

fof(t15_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))))
          & m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))))
          & v23_waybel_0(B,k3_yellow_1(A),k5_yellow_1(A,k2_pre_circ(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(t16_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
         => u1_pre_topc(B) = u1_pre_topc(k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ) )).

fof(t17_waybel18,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) )
         => ( ( u1_struct_0(A) = u1_struct_0(B)
              & u1_pre_topc(A) = u1_pre_topc(B)
              & v2_waybel18(A) )
           => v2_waybel18(B) ) ) ) )).

fof(t18_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel11(B)
            & m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
         => v2_waybel18(B) ) ) )).

fof(t19_waybel18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( ~ v1_xboole_0(B)
          & ? [C] :
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))
              & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_waybel18(B,k2_pre_circ(B,k9_waybel18))))
              & v3_tops_2(k8_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)),C),A,k7_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18)),C)) ) ) ) )).

fof(t20_waybel18,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v2_t_0topsp(A)
        & l1_pre_topc(A) )
     => ~ ( v2_waybel18(A)
          & ! [B] :
              ( ~ v1_xboole_0(B)
             => ~ r1_waybel18(A,k3_waybel18(B,k2_pre_circ(B,k9_waybel18))) ) ) ) )).

fof(dt_k1_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => l1_pre_topc(k1_waybel18(A,B,C)) ) )).

fof(redefinition_k1_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k1_waybel18(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k2_waybel18,axiom,(
    ! [A,B] :
      ( ( v1_waybel18(B)
        & m1_pboole(B,A) )
     => m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) )).

fof(dt_k3_waybel18,axiom,(
    ! [A,B] :
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B))
        & l1_pre_topc(k3_waybel18(A,B)) ) ) )).

fof(dt_k4_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k4_waybel18(A,B,C))
        & l1_pre_topc(k4_waybel18(A,B,C)) ) ) )).

fof(redefinition_k4_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k4_waybel18(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k5_waybel18,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
        & m1_subset_1(D,A) )
     => m1_subset_1(k5_waybel18(A,B,C,D),u1_struct_0(k4_waybel18(A,B,D))) ) )).

fof(redefinition_k5_waybel18,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
        & m1_subset_1(D,A) )
     => k5_waybel18(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k6_waybel18,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k6_waybel18(A,B,C))
        & v1_funct_2(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C)))
        & m2_relset_1(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C))) ) ) )).

fof(dt_k7_waybel18,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_pre_topc(k7_waybel18(A,B,C),B) ) )).

fof(dt_k8_waybel18,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k8_waybel18(A,B,C))
        & v1_funct_2(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C)))
        & m2_relset_1(k8_waybel18(A,B,C),u1_struct_0(A),u1_struct_0(k7_waybel18(A,B,C))) ) ) )).

fof(dt_k9_waybel18,axiom,
    ( v1_pre_topc(k9_waybel18)
    & l1_pre_topc(k9_waybel18) )).

fof(t14_waybel18,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => m2_cantor_1(a_1_0_waybel18(A),k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) )).

fof(fraenkel_a_1_0_waybel18,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_waybel18(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),C,k1_tarski(np__1))) ) ) ) )).
%------------------------------------------------------------------------------