SET007 Axioms: SET007+612.ax


%------------------------------------------------------------------------------
% File     : SET007+612 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of Isomorphism between Relational Structures
% Version  : [Urb08] axioms.
% English  : Some Properties of Isomorphism between Relational Structures On
%            the Product of Topological Spaces

% 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    : yellow14 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   62 (   1 unit)
%            Number of atoms       :  488 (  34 equality)
%            Maximal formula depth :   18 (   9 average)
%            Number of connectives :  506 (  80 ~  ;   0  |; 235  &)
%                                         (   6 <=>; 185 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   63 (   0 propositional; 1-4 arity)
%            Number of functors    :   38 (   2 constant; 0-5 arity)
%            Number of variables   :  180 (   0 singleton; 174 !;   6 ?)
%            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(rc1_yellow14,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & v3_struct_0(A)
      & v1_orders_2(A) ) )).

fof(rc2_yellow14,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & v1_struct_0(A)
      & ~ v3_struct_0(A)
      & v1_monoid_0(A) ) )).

fof(rc3_yellow14,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v1_monoid_0(A) ) )).

fof(cc1_yellow14,axiom,(
    ! [A] :
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( l1_waybel_0(B,A)
         => v1_yellow14(B,A) ) ) )).

fof(rc4_yellow14,axiom,(
    ! [A] :
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( l1_waybel_0(B,A)
          & v6_waybel_0(B,A)
          & v1_yellow14(B,A) ) ) )).

fof(rc5_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_monoid_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( l1_waybel_0(B,A)
          & ~ v3_struct_0(B)
          & v6_waybel_0(B,A)
          & v1_yellow14(B,A) ) ) )).

fof(fc1_yellow14,axiom,(
    ! [A,B] :
      ( ( v1_monoid_0(A)
        & l1_struct_0(A)
        & v1_yellow14(B,A)
        & l1_waybel_0(B,A) )
     => ( v1_relat_1(u1_waybel_0(A,B))
        & v1_funct_1(u1_waybel_0(A,B))
        & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
        & v1_funcop_1(u1_waybel_0(A,B)) ) ) )).

fof(rc6_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_monoid_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( l1_waybel_0(B,A)
          & ~ v3_struct_0(B)
          & v3_orders_2(B)
          & v6_waybel_0(B,A)
          & v7_waybel_0(B)
          & v1_yellow14(B,A) ) ) )).

fof(fc2_yellow14,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ~ v1_xboole_0(k2_relat_1(u1_waybel_0(A,B))) ) )).

fof(fc3_yellow14,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_waybel_0(B,A) )
     => ~ v1_xboole_0(k2_relat_1(k2_waybel_0(A,B))) ) )).

fof(cc2_yellow14,axiom,(
    ! [A,B] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B) )
     => ! [C] :
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v23_waybel_0(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
              & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).

fof(cc3_yellow14,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => ( v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A) ) ) ) )).

fof(cc4_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
           => ( v13_waybel_0(B,A)
              & v1_waybel11(B,A) ) ) ) ) )).

fof(cc5_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_waybel11(A)
        & l1_waybel_9(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v13_waybel_0(B,A)
              & v1_waybel11(B,A) )
           => v3_pre_topc(B,A) ) ) ) )).

fof(fc4_yellow14,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A) )
     => ( v1_relat_1(k4_tmap_1(A,B))
        & v1_funct_1(k4_tmap_1(A,B))
        & ~ v1_xboole_0(k4_tmap_1(A,B))
        & v1_funct_2(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A))
        & v5_pre_topc(k4_tmap_1(A,B),B,A)
        & v1_partfun1(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) )).

fof(fc5_yellow14,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v2_t_0topsp(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B)))
        & v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
        & v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
        & v2_t_0topsp(k3_waybel18(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) )).

fof(fc6_yellow14,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & v1_urysohn1(B)
        & l1_pre_topc(B) )
     => ( ~ v3_struct_0(k3_waybel18(A,k2_pre_circ(A,B)))
        & v1_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
        & v2_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)))
        & v1_urysohn1(k3_waybel18(A,k2_pre_circ(A,B)))
        & v1_monoid_0(k3_waybel18(A,k2_pre_circ(A,B))) ) ) )).

fof(t1_yellow14,axiom,(
    k1_zfmisc_1(np__1) = k2_tarski(np__0,np__1) )).

fof(t2_yellow14,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k2_relat_1(k2_partfun1(A,A,k6_partfun1(A),B)) = B ) )).

fof(t3_yellow14,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_funct_1(k1_funct_4(A,k3_cqc_lang(B,C)),B) = C ) )).

fof(t4_yellow14,axiom,(
    ! [A] :
      ( ( v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( l1_struct_0(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)) )
             => ( k1_yellow_2(A,B,C) = k2_pre_topc(B)
               => v3_struct_0(B) ) ) ) ) )).

fof(t5_yellow14,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( v3_struct_0(B)
            & l1_struct_0(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)) )
             => ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
               => v3_struct_0(A) ) ) ) ) )).

fof(t6_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( l1_struct_0(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)) )
             => ~ ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
                  & v3_struct_0(B) ) ) ) ) )).

fof(t7_yellow14,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(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_yellow_2(u1_struct_0(A),B,C) = k2_pre_topc(B)
                  & v3_struct_0(A) ) ) ) ) )).

fof(d1_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(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)) )
             => ( v22_waybel_0(C,A,B)
              <=> ! [D] :
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r4_waybel_0(A,B,C,D) ) ) ) ) ) )).

fof(d2_yellow14,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_waybel_0(B,A)
         => ( v1_yellow14(B,A)
          <=> v1_funcop_1(u1_waybel_0(A,B)) ) ) ) )).

fof(t8_yellow14,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) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ! [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(A),u1_struct_0(B))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
                         => ( ( r1_yellow_2(u1_struct_0(A),B,E,F)
                              & v5_orders_3(D,B,C) )
                           => r1_yellow_2(u1_struct_0(A),C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),E,D),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,D)) ) ) ) ) ) ) ) )).

fof(t9_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_waybel_9(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( 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] :
                      ( m1_subset_1(E,u1_struct_0(k3_waybel24(A,B)))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(k3_waybel24(A,B)))
                         => ( ( E = C
                              & F = D )
                           => ( r1_orders_2(k3_waybel24(A,B),E,F)
                            <=> r1_yellow_2(u1_struct_0(A),B,C,D) ) ) ) ) ) ) ) ) )).

fof(t10_yellow14,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v23_waybel_0(C,A,B)
               => v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).

fof(t11_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(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)) )
             => ( v23_waybel_0(C,A,B)
               => v23_waybel_0(k2_tops_2(A,B,C),B,A) ) ) ) ) )).

fof(t12_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v2_lattice3(A) )
           => v2_lattice3(B) ) ) ) )).

fof(t13_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ( ( r5_waybel_1(A,B)
              & v1_lattice3(A) )
           => v1_lattice3(B) ) ) ) )).

fof(t14_yellow14,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v3_yellow_0(A) ) ) )).

fof(t15_yellow14,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( r5_waybel_1(A,B)
              & v1_yellow_0(A) )
           => v1_yellow_0(B) ) ) ) )).

fof(t16_yellow14,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( r5_waybel_1(A,B)
              & v2_yellow_0(A) )
           => v2_yellow_0(B) ) ) ) )).

fof(t17_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [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)) )
                 => ( ( v23_waybel_0(D,A,B)
                      & r1_yellow_0(A,C) )
                   => r1_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ) )).

fof(t18_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [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)) )
                 => ( ( v23_waybel_0(D,A,B)
                      & r2_yellow_0(A,C) )
                   => r2_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ) )).

fof(t19_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ~ ( ~ r1_t_0topsp(A,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)) )
                   => ~ ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = k2_pre_topc(A)
                        & k1_yellow_2(A,B,C) = k2_pre_topc(B) ) ) )
           => ( v3_struct_0(A)
            <=> v3_struct_0(B) ) ) ) ) )).

fof(t20_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => r1_t_0topsp(A,g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) )).

fof(t21_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( D = k1_tarski(B)
                          & r1_tarski(k6_pre_topc(A,D),k6_pre_topc(A,E)) )
                       => r2_hidden(B,k6_pre_topc(A,E)) ) ) ) ) ) ) )).

fof(t22_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( D = k1_tarski(C)
                          & r2_hidden(B,k6_pre_topc(A,D))
                          & v3_pre_topc(E,A)
                          & r2_hidden(B,E) )
                       => r2_hidden(C,E) ) ) ) ) ) ) )).

fof(t23_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( D = k1_tarski(B)
                          & E = k1_tarski(C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( v3_pre_topc(F,A)
                                  & r2_hidden(B,F) )
                               => r2_hidden(C,F) ) ) )
                       => r1_tarski(k6_pre_topc(A,D),k6_pre_topc(A,E)) ) ) ) ) ) ) )).

fof(t24_yellow14,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] :
              ( ( v2_yellow_8(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
                   => v2_yellow_8(D,B) ) ) ) ) ) )).

fof(t25_yellow14,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] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
                         => ( ( C = D
                              & E = F
                              & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                              & r1_yellow_8(A,E,C) )
                           => r1_yellow_8(B,F,D) ) ) ) ) ) ) ) )).

fof(t26_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( C = D
                      & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
                      & v6_compts_1(C,A) )
                   => v6_compts_1(D,B) ) ) ) ) ) )).

fof(t27_yellow14,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) )
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v3_yellow_8(A) )
           => v3_yellow_8(B) ) ) ) )).

fof(t28_yellow14,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) )
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v6_waybel_3(A) )
           => v6_waybel_3(B) ) ) ) )).

fof(t29_yellow14,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( l1_pre_topc(B)
         => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
              & v2_compts_1(A) )
           => v2_compts_1(B) ) ) ) )).

fof(t30_yellow14,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,B)))
                 => ( r2_hidden(C,k6_pre_topc(k3_waybel18(A,B),k1_struct_0(k3_waybel18(A,B),D)))
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => r2_hidden(k5_waybel18(A,B,C,E),k6_pre_topc(k4_waybel18(A,B,E),k1_struct_0(k4_waybel18(A,B,E),k5_waybel18(A,B,D,E)))) ) ) ) ) ) ) )).

fof(t31_yellow14,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
                 => ( r2_hidden(C,k6_pre_topc(k3_waybel18(A,k2_pre_circ(A,B)),k1_struct_0(k3_waybel18(A,k2_pre_circ(A,B)),D)))
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => r2_hidden(k2_yellow14(A,B,C,E),k6_pre_topc(B,k1_struct_0(B,k2_yellow14(A,B,D,E)))) ) ) ) ) ) ) )).

fof(t32_yellow14,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v4_waybel_3(C)
                & v1_waybel18(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,C)))
                 => k5_card_3(B,k6_pre_topc(k3_waybel18(A,C),k1_struct_0(k3_waybel18(A,C),D))) = k6_pre_topc(k4_waybel18(A,C,B),k1_struct_0(k4_waybel18(A,C,B),k5_waybel18(A,C,D,B))) ) ) ) ) )).

fof(t33_yellow14,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v2_pre_topc(C)
                & l1_pre_topc(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,C))))
                 => k5_card_3(B,k6_pre_topc(k3_waybel18(A,k2_pre_circ(A,C)),k1_struct_0(k3_waybel18(A,k2_pre_circ(A,C)),D))) = k6_pre_topc(C,k1_struct_0(C,k2_yellow14(A,C,D,B))) ) ) ) ) )).

fof(t34_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(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)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( ( C = k7_grcat_1(A)
                      & D = k7_grcat_1(A)
                      & v5_pre_topc(C,A,B)
                      & v5_pre_topc(D,B,A) )
                   => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ) ) )).

fof(t35_yellow14,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(k8_waybel18(A,B,C),A,k7_waybel18(A,B,C))
               => v5_pre_topc(C,A,B) ) ) ) ) )).

fof(t36_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,B) = B
           => k7_funct_2(u1_struct_0(k7_waybel18(A,A,B)),u1_struct_0(A),u1_struct_0(k7_waybel18(A,A,B)),k4_tmap_1(A,k7_waybel18(A,A,B)),k8_waybel18(A,A,B)) = k7_grcat_1(k7_waybel18(A,A,B)) ) ) ) )).

fof(t37_yellow14,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => v3_tops_2(k8_waybel18(B,A,k4_tmap_1(A,B)),B,k7_waybel18(B,A,k4_tmap_1(A,B))) ) ) )).

fof(t38_yellow14,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_pre_topc(k4_waybel18(A,B,C))
                  & v2_t_0topsp(k4_waybel18(A,B,C))
                  & l1_pre_topc(k4_waybel18(A,B,C)) ) )
           => v2_t_0topsp(k3_waybel18(A,B)) ) ) ) )).

fof(t39_yellow14,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ( ! [C] :
                ( m1_subset_1(C,A)
               => ( v1_urysohn1(k4_waybel18(A,B,C))
                  & v2_pre_topc(k4_waybel18(A,B,C)) ) )
           => v1_urysohn1(k3_waybel18(A,B)) ) ) ) )).

fof(dt_k1_yellow14,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_yellow14(A,B,C,D),u1_struct_0(B)) ) )).

fof(redefinition_k1_yellow14,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_yellow14(A,B,C,D) = k1_funct_1(C,D) ) )).

fof(dt_k2_yellow14,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
        & m1_subset_1(D,A) )
     => m1_subset_1(k2_yellow14(A,B,C,D),u1_struct_0(B)) ) )).

fof(redefinition_k2_yellow14,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,k2_pre_circ(A,B))))
        & m1_subset_1(D,A) )
     => k2_yellow14(A,B,C,D) = k1_funct_1(C,D) ) )).
%------------------------------------------------------------------------------