SET007 Axioms: SET007+418.ax


%------------------------------------------------------------------------------
% File     : SET007+418 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Bounding Boxes for Compact Sets in E^2
% 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    : pscomp_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  262 (  14 unit)
%            Number of atoms       : 1224 ( 159 equality)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives : 1079 ( 117 ~  ;   2  |; 517  &)
%                                         (  44 <=>; 399 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   60 (   1 propositional; 0-3 arity)
%            Number of functors    :   90 (  10 constant; 0-4 arity)
%            Number of variables   :  435 (   0 singleton; 412 !;  23 ?)
%            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(fc1_pscomp_1,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers)
    & ~ v1_setfam_1(k1_numbers) )).

fof(fc2_pscomp_1,axiom,
    ( ~ v1_xboole_0(k5_ordinal2)
    & v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2)
    & ~ v1_setfam_1(k5_ordinal2) )).

fof(rc1_pscomp_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) )).

fof(rc2_pscomp_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & ~ v1_setfam_1(A) ) )).

fof(rc3_pscomp_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_setfam_1(A) ) )).

fof(rc4_pscomp_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v1_setfam_1(A) ) )).

fof(cc1_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v6_ordinal1(B)
          & v1_setfam_1(B) )
       => v1_compts_1(B) ) ) )).

fof(fc3_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ~ v1_xboole_0(k9_relat_1(C,A)) ) )).

fof(rc5_pscomp_1,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_seq_4(A)
      & v2_rcomp_1(A) ) )).

fof(fc4_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ~ v1_xboole_0(k5_pscomp_1(A))
        & v1_membered(k5_pscomp_1(A))
        & v2_membered(k5_pscomp_1(A)) ) ) )).

fof(fc5_pscomp_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers))
        & m1_subset_1(B,k1_numbers) )
     => ( ~ v1_xboole_0(k8_measure6(A,B))
        & v1_membered(k8_measure6(A,B))
        & v2_membered(k8_measure6(A,B)) ) ) )).

fof(fc6_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ~ v1_xboole_0(k6_pscomp_1(A))
        & v1_membered(k6_pscomp_1(A))
        & v2_membered(k6_pscomp_1(A))
        & v1_setfam_1(k6_pscomp_1(A)) ) ) )).

fof(fc7_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_setfam_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_membered(k6_pscomp_1(A))
        & v2_membered(k6_pscomp_1(A))
        & v1_setfam_1(k6_pscomp_1(A)) ) ) )).

fof(fc8_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(k7_pscomp_1(A))
        & v2_membered(k7_pscomp_1(A))
        & v2_rcomp_1(k7_pscomp_1(A)) ) ) )).

fof(rc6_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),k1_numbers)
          & v1_seq_1(B)
          & v1_seq_2(B)
          & v2_seq_2(B)
          & v3_seq_2(B)
          & v1_partfun1(B,u1_struct_0(A),k1_numbers) ) ) )).

fof(rc7_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),k1_numbers)
          & v1_seq_1(B)
          & v1_partfun1(B,u1_struct_0(A),k1_numbers)
          & v9_pscomp_1(B,A) ) ) )).

fof(rc8_pscomp_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A) )
     => ? [C] :
          ( m1_relset_1(C,u1_struct_0(B),k1_numbers)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(B),k1_numbers)
          & v1_seq_1(C)
          & v1_partfun1(C,u1_struct_0(B),k1_numbers)
          & v9_pscomp_1(C,B) ) ) )).

fof(rc9_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v6_compts_1(B,A) ) ) )).

fof(fc9_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & v9_pscomp_1(B,A)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_relat_1(k15_pscomp_1(A,C,B))
        & v1_funct_1(k15_pscomp_1(A,C,B))
        & v1_funct_2(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
        & v1_seq_1(k15_pscomp_1(A,C,B))
        & v1_partfun1(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
        & v9_pscomp_1(k15_pscomp_1(A,C,B),k3_pre_topc(A,C)) ) ) )).

fof(fc10_pscomp_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & v6_compts_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v3_struct_0(k3_pre_topc(A,B))
        & v1_pre_topc(k3_pre_topc(A,B))
        & v2_pre_topc(k3_pre_topc(A,B))
        & v2_compts_1(k3_pre_topc(A,B)) ) ) )).

fof(cc2_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v10_pscomp_1(A) ) ) ) )).

fof(rc10_pscomp_1,axiom,(
    ? [A] :
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v2_compts_1(A)
      & v10_pscomp_1(A) ) )).

fof(cc3_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v10_pscomp_1(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_relset_1(B,u1_struct_0(A),k1_numbers)
         => ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & v9_pscomp_1(B,A) )
           => ( ~ v1_xboole_0(B)
              & v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & v1_seq_1(B)
              & v3_seq_2(B)
              & v1_partfun1(B,u1_struct_0(A),k1_numbers)
              & v7_pscomp_1(B,u1_struct_0(A))
              & v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) )).

fof(fc11_pscomp_1,axiom,
    ( ~ v1_xboole_0(k16_pscomp_1)
    & v1_relat_1(k16_pscomp_1)
    & v1_funct_1(k16_pscomp_1)
    & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & v1_seq_1(k16_pscomp_1)
    & v1_partfun1(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & v9_pscomp_1(k16_pscomp_1,k15_euclid(np__2)) )).

fof(fc12_pscomp_1,axiom,
    ( ~ v1_xboole_0(k17_pscomp_1)
    & v1_relat_1(k17_pscomp_1)
    & v1_funct_1(k17_pscomp_1)
    & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & v1_seq_1(k17_pscomp_1)
    & v1_partfun1(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & v9_pscomp_1(k17_pscomp_1,k15_euclid(np__2)) )).

fof(fc13_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k26_pscomp_1(A))
        & v6_compts_1(k26_pscomp_1(A),k15_euclid(np__2)) ) ) )).

fof(fc14_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k27_pscomp_1(A))
        & v6_compts_1(k27_pscomp_1(A),k15_euclid(np__2)) ) ) )).

fof(fc15_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k28_pscomp_1(A))
        & v6_compts_1(k28_pscomp_1(A),k15_euclid(np__2)) ) ) )).

fof(fc16_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( ~ v1_xboole_0(k29_pscomp_1(A))
        & v6_compts_1(k29_pscomp_1(A),k15_euclid(np__2)) ) ) )).

fof(d1_pscomp_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
    <=> ~ r2_hidden(np__0,A) ) )).

fof(t1_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_setfam_1(A)
        & v6_ordinal1(A) )
     => ( v1_xboole_0(A)
        | v1_compts_1(A) ) ) )).

fof(d2_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,k1_pcomps_1(B),k1_pcomps_1(A))
            & m2_relset_1(D,k1_pcomps_1(B),k1_pcomps_1(A)) )
         => ( D = k2_pscomp_1(A,B,C)
          <=> ! [E] :
                ( m1_subset_1(E,k1_zfmisc_1(B))
               => k8_funct_2(k1_zfmisc_1(B),k1_pcomps_1(A),D,E) = k3_funct_2(A,B,C,E) ) ) ) ) )).

fof(t2_pscomp_1,axiom,(
    ! [A,B,C,D] :
      ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
     => ! [E] :
          ( ( v1_funct_1(E)
            & v1_funct_2(E,A,B)
            & m2_relset_1(E,A,B) )
         => ( r2_hidden(C,k6_setfam_1(A,k2_funct_2(k1_pcomps_1(B),k1_pcomps_1(A),k2_pscomp_1(A,B,E),D)))
           => r2_hidden(k1_funct_1(E,C),k6_setfam_1(B,D)) ) ) ) )).

fof(t3_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( k3_real_1(k18_complex1(A),k18_complex1(B)) = np__0
           => A = np__0 ) ) ) )).

fof(t4_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(B,A)
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k3_real_1(k18_complex1(A),k18_complex1(C)),k18_complex1(B)) ) ) ) ) )).

fof(t5_pscomp_1,axiom,(
    $true )).

fof(t6_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ~ ( v4_seq_2(A)
          & v2_relat_1(A)
          & k2_seq_2(A) = np__0
          & v3_seq_2(k18_seq_1(A)) ) ) )).

fof(t7_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v3_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A))
      <=> v3_seq_2(A) ) ) )).

fof(d3_pscomp_1,axiom,(
    ! [A] :
      ( v2_membered(A)
     => ( v1_pscomp_1(A)
      <=> ( v1_seq_4(A)
          & r2_hidden(k2_seq_4(A),A) ) ) ) )).

fof(d4_pscomp_1,axiom,(
    ! [A] :
      ( v2_membered(A)
     => ( v2_pscomp_1(A)
      <=> ( v2_seq_4(A)
          & r2_hidden(k3_seq_4(A),A) ) ) ) )).

fof(d5_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
     => ( v3_pscomp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
           => ( r2_hidden(B,A)
             => v3_rcomp_1(B) ) ) ) ) )).

fof(d6_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
     => ( v4_pscomp_1(A)
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
           => ( r2_hidden(B,A)
             => v2_rcomp_1(B) ) ) ) ) )).

fof(t8_pscomp_1,axiom,(
    $true )).

fof(t9_pscomp_1,axiom,(
    $true )).

fof(t10_pscomp_1,axiom,(
    $true )).

fof(t11_pscomp_1,axiom,(
    $true )).

fof(t12_pscomp_1,axiom,(
    $true )).

fof(t13_pscomp_1,axiom,(
    $true )).

fof(t14_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( r2_hidden(A,B)
          <=> r2_hidden(k4_xcmplx_0(A),k5_pscomp_1(B)) ) ) ) )).

fof(t15_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_seq_4(A)
      <=> v2_seq_4(k5_pscomp_1(A)) ) ) )).

fof(t16_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v2_seq_4(A)
      <=> v1_seq_4(k5_pscomp_1(A)) ) ) )).

fof(t17_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v2_seq_4(A)
       => k4_pscomp_1(A) = k1_real_1(k3_pscomp_1(k5_pscomp_1(A))) ) ) )).

fof(t18_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( v1_seq_4(A)
       => k3_pscomp_1(A) = k1_real_1(k4_pscomp_1(k5_pscomp_1(A))) ) ) )).

fof(t19_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v2_rcomp_1(A)
      <=> v2_rcomp_1(k5_pscomp_1(A)) ) ) )).

fof(t20_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( r2_hidden(A,B)
              <=> r2_hidden(k2_xcmplx_0(C,A),k8_measure6(B,C)) ) ) ) ) )).

fof(t21_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => A = k8_measure6(A,np__0) ) )).

fof(t22_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => k8_measure6(k8_measure6(A,C),B) = k8_measure6(A,k3_real_1(B,C)) ) ) ) )).

fof(t23_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v1_seq_4(A)
          <=> v1_seq_4(k8_measure6(A,B)) ) ) ) )).

fof(t24_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v2_seq_4(A)
          <=> v2_seq_4(k8_measure6(A,B)) ) ) ) )).

fof(t25_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( v2_seq_4(B)
           => k4_pscomp_1(k8_measure6(B,A)) = k3_real_1(A,k4_pscomp_1(B)) ) ) ) )).

fof(t26_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( v1_seq_4(B)
           => k3_pscomp_1(k8_measure6(B,A)) = k3_real_1(A,k3_pscomp_1(B)) ) ) ) )).

fof(t27_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( v2_rcomp_1(A)
          <=> v2_rcomp_1(k8_measure6(A,B)) ) ) ) )).

fof(t28_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( ( v1_setfam_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( r2_hidden(A,B)
          <=> r2_hidden(k7_xcmplx_0(np__1,A),k6_pscomp_1(B)) ) ) ) )).

fof(t29_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_setfam_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => k6_pscomp_1(k6_pscomp_1(A)) = A ) )).

fof(t30_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_setfam_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
     => ( ( v2_rcomp_1(A)
          & v3_seq_4(A) )
       => v2_rcomp_1(k6_pscomp_1(A)) ) ) )).

fof(t31_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
     => ( v4_pscomp_1(A)
       => v2_rcomp_1(k6_setfam_1(k1_numbers,A)) ) ) )).

fof(t32_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( ( v2_rcomp_1(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
         => ( r1_tarski(A,B)
           => r1_tarski(k7_pscomp_1(A),B) ) ) ) )).

fof(t33_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => r1_tarski(A,k7_pscomp_1(A)) ) )).

fof(t34_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v2_rcomp_1(A)
      <=> A = k7_pscomp_1(A) ) ) )).

fof(t35_pscomp_1,axiom,(
    k7_pscomp_1(k1_subset_1(k1_numbers)) = k1_xboole_0 )).

fof(t36_pscomp_1,axiom,(
    k7_pscomp_1(k2_subset_1(k1_numbers)) = k1_numbers )).

fof(t37_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ( r1_tarski(A,B)
           => r1_tarski(k7_pscomp_1(A),k7_pscomp_1(B)) ) ) ) )).

fof(t38_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ( r2_hidden(B,k7_pscomp_1(A))
          <=> ! [C] :
                ( ( v3_rcomp_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
               => ~ ( r2_hidden(B,C)
                    & v1_xboole_0(k5_subset_1(k1_numbers,C,A)) ) ) ) ) ) )).

fof(t39_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ~ ( r2_hidden(B,k7_pscomp_1(A))
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ~ ( r1_tarski(k1_pscomp_1(k5_numbers,k1_numbers,C),A)
                      & v4_seq_2(C)
                      & k2_seq_2(C) = B ) ) ) ) ) )).

fof(d11_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ( v2_seq_2(B)
      <=> v2_seq_4(k2_funct_2(A,k1_numbers,B,A)) ) ) )).

fof(d12_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ( v1_seq_2(B)
      <=> v1_seq_4(k2_funct_2(A,k1_numbers,B,A)) ) ) )).

fof(d13_pscomp_1,axiom,(
    $true )).

fof(d14_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ( v7_pscomp_1(B,A)
      <=> v1_pscomp_1(k2_funct_2(A,k1_numbers,B,A)) ) ) )).

fof(d15_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ( v8_pscomp_1(B,A)
      <=> v2_pscomp_1(k2_funct_2(A,k1_numbers,B,A)) ) ) )).

fof(d16_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => ( C = k8_pscomp_1(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k2_seq_1(A,k1_numbers,C,D) = k1_real_1(k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) )).

fof(t40_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,k1_numbers)
        & m2_relset_1(C,A,k1_numbers) )
     => k2_funct_2(A,k1_numbers,k8_pscomp_1(A,C),B) = k5_pscomp_1(k2_funct_2(A,k1_numbers,C,B)) ) )).

fof(t41_pscomp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v8_pscomp_1(B,A)
          <=> v7_pscomp_1(k8_pscomp_1(A,B),A) ) ) ) )).

fof(t42_pscomp_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k1_numbers)
            & m2_relset_1(B,A,k1_numbers) )
         => ( v7_pscomp_1(B,A)
          <=> v8_pscomp_1(k8_pscomp_1(A,B),A) ) ) ) )).

fof(t43_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => k3_funct_2(A,k1_numbers,k8_pscomp_1(A,C),B) = k3_funct_2(A,k1_numbers,C,k5_pscomp_1(B)) ) ) )).

fof(d17_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_numbers)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,k1_numbers)
                & m2_relset_1(D,A,k1_numbers) )
             => ( D = k9_pscomp_1(A,B,C)
              <=> ! [E] :
                    ( r2_hidden(E,A)
                   => k2_seq_1(A,k1_numbers,D,E) = k3_real_1(B,k2_seq_1(A,k1_numbers,C,E)) ) ) ) ) ) )).

fof(t44_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,k1_numbers)
        & m2_relset_1(C,A,k1_numbers) )
     => ! [D] :
          ( m1_subset_1(D,k1_numbers)
         => k2_funct_2(A,k1_numbers,k9_pscomp_1(A,D,C),B) = k8_measure6(k2_funct_2(A,k1_numbers,C,B),D) ) ) )).

fof(t45_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => ! [D] :
              ( m1_subset_1(D,k1_numbers)
             => k3_funct_2(A,k1_numbers,k9_pscomp_1(A,D,C),B) = k3_funct_2(A,k1_numbers,C,k8_measure6(B,k1_real_1(D))) ) ) ) )).

fof(d18_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m2_relset_1(B,A,k1_numbers) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => ( C = k10_pscomp_1(A,B)
          <=> ! [D] :
                ( r2_hidden(D,A)
               => k2_seq_1(A,k1_numbers,C,D) = k6_real_1(np__1,k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) )).

fof(t46_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k1_numbers)
            & m2_relset_1(C,A,k1_numbers) )
         => k3_funct_2(A,k1_numbers,k10_pscomp_1(A,C),B) = k3_funct_2(A,k1_numbers,C,k6_pscomp_1(B)) ) ) )).

fof(d19_pscomp_1,axiom,(
    $true )).

fof(d20_pscomp_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => k12_pscomp_1(A,B) = k4_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) )).

fof(d21_pscomp_1,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => k13_pscomp_1(A,B) = k3_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) )).

fof(t47_pscomp_1,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),k1_numbers)
            & v2_seq_2(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_xreal_0(k12_pscomp_1(A,B),k2_seq_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) )).

fof(t48_pscomp_1,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),k1_numbers)
            & v2_seq_2(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_xreal_0(C,k2_seq_1(u1_struct_0(A),k1_numbers,B,D)) )
               => r1_xreal_0(C,k12_pscomp_1(A,B)) ) ) ) ) )).

fof(t49_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(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),k1_numbers)
                & m2_relset_1(C,u1_struct_0(B),k1_numbers) )
             => ( ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => r1_xreal_0(A,k2_seq_1(u1_struct_0(B),k1_numbers,C,D)) )
                  & ! [D] :
                      ( v1_xreal_0(D)
                     => ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => r1_xreal_0(D,k2_seq_1(u1_struct_0(B),k1_numbers,C,E)) )
                       => r1_xreal_0(D,A) ) ) )
               => A = k12_pscomp_1(B,C) ) ) ) ) )).

fof(t50_pscomp_1,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),k1_numbers)
            & v1_seq_2(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_xreal_0(k2_seq_1(u1_struct_0(A),k1_numbers,B,C),k13_pscomp_1(A,B)) ) ) ) )).

fof(t51_pscomp_1,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),k1_numbers)
            & v1_seq_2(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r1_xreal_0(k2_seq_1(u1_struct_0(A),k1_numbers,B,D),C) )
               => r1_xreal_0(k13_pscomp_1(A,B),C) ) ) ) ) )).

fof(t52_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(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),k1_numbers)
                & m2_relset_1(C,u1_struct_0(B),k1_numbers) )
             => ( ( ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => r1_xreal_0(k2_seq_1(u1_struct_0(B),k1_numbers,C,D),A) )
                  & ! [D] :
                      ( v1_xreal_0(D)
                     => ( ! [E] :
                            ( m1_subset_1(E,u1_struct_0(B))
                           => r1_xreal_0(k2_seq_1(u1_struct_0(B),k1_numbers,C,E),D) )
                       => r1_xreal_0(A,D) ) ) )
               => A = k13_pscomp_1(B,C) ) ) ) ) )).

fof(t53_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & v3_seq_2(B)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => r1_xreal_0(k12_pscomp_1(A,B),k13_pscomp_1(A,B)) ) ) )).

fof(d22_pscomp_1,axiom,(
    $true )).

fof(d23_pscomp_1,axiom,(
    $true )).

fof(d24_pscomp_1,axiom,(
    $true )).

fof(d25_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ( v9_pscomp_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( v2_rcomp_1(C)
                 => v4_pre_topc(k11_pscomp_1(A,B,C),A) ) ) ) ) ) )).

fof(t54_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ( v9_pscomp_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
               => ( v3_rcomp_1(C)
                 => v3_pre_topc(k11_pscomp_1(A,B,C),A) ) ) ) ) ) )).

fof(t55_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ( v9_pscomp_1(B,A)
           => v9_pscomp_1(k8_pscomp_1(u1_struct_0(A),B),A) ) ) ) )).

fof(t56_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( l1_pre_topc(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),k1_numbers)
                & m2_relset_1(C,u1_struct_0(B),k1_numbers) )
             => ( v9_pscomp_1(C,B)
               => v9_pscomp_1(k9_pscomp_1(u1_struct_0(B),A,C),B) ) ) ) ) )).

fof(t57_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ( v9_pscomp_1(B,A)
           => ( r2_hidden(np__0,k1_pscomp_1(u1_struct_0(A),k1_numbers,B))
              | v9_pscomp_1(k10_pscomp_1(u1_struct_0(A),B),A) ) ) ) ) )).

fof(t58_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
             => ( ( v9_pscomp_1(B,A)
                  & v3_pscomp_1(C) )
               => v1_tops_2(k14_pscomp_1(k1_numbers,u1_struct_0(A),k2_pscomp_1(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) )).

fof(t59_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),k1_numbers)
            & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
             => ( ( v9_pscomp_1(B,A)
                  & v4_pscomp_1(C) )
               => v2_tops_2(k14_pscomp_1(k1_numbers,u1_struct_0(A),k2_pscomp_1(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) )).

fof(d26_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),k1_numbers)
                & m2_relset_1(C,u1_struct_0(A),k1_numbers) )
             => k15_pscomp_1(A,B,C) = k7_relat_1(C,B) ) ) ) )).

fof(t60_pscomp_1,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),k1_numbers)
              & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
           => ( v9_pscomp_1(B,A)
             => v7_pscomp_1(B,u1_struct_0(A)) ) )
      <=> ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
           => ( v9_pscomp_1(B,A)
             => v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) )).

fof(t61_pscomp_1,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),k1_numbers)
              & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
           => ( v9_pscomp_1(B,A)
             => v3_seq_2(B) ) )
      <=> ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
           => ( v9_pscomp_1(B,A)
             => v7_pscomp_1(B,u1_struct_0(A)) ) ) ) ) )).

fof(d27_pscomp_1,axiom,(
    ! [A] :
      ( l1_pre_topc(A)
     => ( v10_pscomp_1(A)
      <=> ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),k1_numbers)
              & m2_relset_1(B,u1_struct_0(A),k1_numbers) )
           => ( v9_pscomp_1(B,A)
             => v3_seq_2(B) ) ) ) ) )).

fof(t62_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v6_compts_1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                    & v9_pscomp_1(D,A)
                    & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                 => ( r1_tarski(B,C)
                   => r1_xreal_0(k12_pscomp_1(k3_pre_topc(A,C),k15_pscomp_1(A,C,D)),k12_pscomp_1(k3_pre_topc(A,B),k15_pscomp_1(A,B,D))) ) ) ) ) ) )).

fof(t63_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] :
              ( ( v6_compts_1(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),k1_numbers)
                    & v9_pscomp_1(D,A)
                    & m2_relset_1(D,u1_struct_0(A),k1_numbers) )
                 => ( r1_tarski(B,C)
                   => r1_xreal_0(k13_pscomp_1(k3_pre_topc(A,B),k15_pscomp_1(A,B,D)),k13_pscomp_1(k3_pre_topc(A,C),k15_pscomp_1(A,C,D))) ) ) ) ) ) )).

fof(t64_pscomp_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v6_compts_1(B,k15_euclid(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
         => ! [C] :
              ( ( v6_compts_1(C,k15_euclid(A))
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
             => v6_compts_1(k5_subset_1(u1_struct_0(k15_euclid(A)),B,C),k15_euclid(A)) ) ) ) )).

fof(d28_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),k1_numbers)
        & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),k1_numbers) )
     => ( A = k16_pscomp_1
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => k2_seq_1(u1_struct_0(k15_euclid(np__2)),k1_numbers,A,B) = k21_euclid(B) ) ) ) )).

fof(d29_pscomp_1,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),k1_numbers)
        & m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),k1_numbers) )
     => ( A = k17_pscomp_1
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
           => k2_seq_1(u1_struct_0(k15_euclid(np__2)),k1_numbers,A,B) = k22_euclid(B) ) ) ) )).

fof(t69_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,A)
           => k2_seq_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),k1_numbers,k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1),B) = k21_euclid(B) ) ) ) )).

fof(t70_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
         => ( r2_hidden(B,A)
           => k2_seq_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),k1_numbers,k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1),B) = k22_euclid(B) ) ) ) )).

fof(d30_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k18_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1)) ) )).

fof(d31_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k19_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1)) ) )).

fof(d32_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k20_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1)) ) )).

fof(d33_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1)) ) )).

fof(t71_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v6_compts_1(B,k15_euclid(np__2))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,B)
           => ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A))
              & r1_xreal_0(k21_euclid(A),k20_pscomp_1(B))
              & r1_xreal_0(k21_pscomp_1(B),k22_euclid(A))
              & r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) )).

fof(d34_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k21_pscomp_1(A)) ) )).

fof(d35_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k23_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k19_pscomp_1(A)) ) )).

fof(d36_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k24_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k19_pscomp_1(A)) ) )).

fof(d37_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k25_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k21_pscomp_1(A)) ) )).

fof(t72_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k22_pscomp_1(A)) = k18_pscomp_1(A) ) )).

fof(t73_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k22_pscomp_1(A)) = k21_pscomp_1(A) ) )).

fof(t74_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k23_pscomp_1(A)) = k18_pscomp_1(A) ) )).

fof(t75_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k23_pscomp_1(A)) = k19_pscomp_1(A) ) )).

fof(t76_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k24_pscomp_1(A)) = k20_pscomp_1(A) ) )).

fof(t77_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k24_pscomp_1(A)) = k19_pscomp_1(A) ) )).

fof(t78_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k25_pscomp_1(A)) = k20_pscomp_1(A) ) )).

fof(t79_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k25_pscomp_1(A)) = k21_pscomp_1(A) ) )).

fof(t80_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k22_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A)) ) )).

fof(t81_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k21_euclid(k25_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A)) ) )).

fof(t82_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k23_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A)) ) )).

fof(t83_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k22_euclid(k22_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A)) ) )).

fof(d38_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k26_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),A) ) )).

fof(d39_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k27_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)),A) ) )).

fof(d40_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k28_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),A) ) )).

fof(d41_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k29_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),A) ) )).

fof(d42_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k30_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))) ) )).

fof(d43_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k31_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))) ) )).

fof(d44_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k32_pscomp_1(A) = k23_euclid(k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) )).

fof(d45_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k33_pscomp_1(A) = k23_euclid(k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) )).

fof(d46_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k34_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))) ) )).

fof(d47_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k35_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))) ) )).

fof(d48_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k36_pscomp_1(A) = k23_euclid(k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)),k21_pscomp_1(A)) ) )).

fof(d49_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => k37_pscomp_1(A) = k23_euclid(k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)),k21_pscomp_1(A)) ) )).

fof(t84_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k30_pscomp_1(A)) = k18_pscomp_1(A)
        & k21_euclid(k31_pscomp_1(A)) = k18_pscomp_1(A) ) ) )).

fof(t85_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k22_pscomp_1(A)) = k21_euclid(k30_pscomp_1(A))
        & k21_euclid(k22_pscomp_1(A)) = k21_euclid(k31_pscomp_1(A))
        & k21_euclid(k30_pscomp_1(A)) = k21_euclid(k31_pscomp_1(A))
        & k21_euclid(k30_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A))
        & k21_euclid(k31_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A)) ) ) )).

fof(t86_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k30_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))
        & k22_euclid(k31_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1)) ) ) )).

fof(t87_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k30_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k31_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k23_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k30_pscomp_1(A)),k22_euclid(k31_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k30_pscomp_1(A)),k22_euclid(k23_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k31_pscomp_1(A)),k22_euclid(k23_pscomp_1(A))) ) ) )).

fof(t88_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k26_pscomp_1(B))
           => ( k21_euclid(A) = k21_euclid(k30_pscomp_1(B))
              & ( v6_compts_1(B,k15_euclid(np__2))
               => ( r1_xreal_0(k22_euclid(k30_pscomp_1(B)),k22_euclid(A))
                  & r1_xreal_0(k22_euclid(A),k22_euclid(k31_pscomp_1(B))) ) ) ) ) ) ) )).

fof(t89_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k26_pscomp_1(A),k3_topreal1(np__2,k30_pscomp_1(A),k31_pscomp_1(A))) ) )).

fof(t90_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k3_topreal1(np__2,k30_pscomp_1(A),k31_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A))) ) )).

fof(t91_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r2_hidden(k30_pscomp_1(A),k26_pscomp_1(A))
        & r2_hidden(k31_pscomp_1(A),k26_pscomp_1(A)) ) ) )).

fof(t92_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k30_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k30_pscomp_1(A))
        & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k31_pscomp_1(A),k23_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k31_pscomp_1(A)) ) ) )).

fof(t93_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k30_pscomp_1(A) = k31_pscomp_1(A)
       => k26_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k30_pscomp_1(A)) ) ) )).

fof(t94_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k32_pscomp_1(A)) = k19_pscomp_1(A)
        & k22_euclid(k33_pscomp_1(A)) = k19_pscomp_1(A) ) ) )).

fof(t95_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k23_pscomp_1(A)) = k22_euclid(k32_pscomp_1(A))
        & k22_euclid(k23_pscomp_1(A)) = k22_euclid(k33_pscomp_1(A))
        & k22_euclid(k32_pscomp_1(A)) = k22_euclid(k33_pscomp_1(A))
        & k22_euclid(k32_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A))
        & k22_euclid(k33_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A)) ) ) )).

fof(t96_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k32_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1))
        & k21_euclid(k33_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)) ) ) )).

fof(t97_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k32_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k33_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k24_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k32_pscomp_1(A)),k21_euclid(k33_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k32_pscomp_1(A)),k21_euclid(k24_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k33_pscomp_1(A)),k21_euclid(k24_pscomp_1(A))) ) ) )).

fof(t98_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k27_pscomp_1(B))
           => ( k22_euclid(A) = k22_euclid(k32_pscomp_1(B))
              & ( v6_compts_1(B,k15_euclid(np__2))
               => ( r1_xreal_0(k21_euclid(k32_pscomp_1(B)),k21_euclid(A))
                  & r1_xreal_0(k21_euclid(A),k21_euclid(k33_pscomp_1(B))) ) ) ) ) ) ) )).

fof(t99_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k27_pscomp_1(A),k3_topreal1(np__2,k32_pscomp_1(A),k33_pscomp_1(A))) ) )).

fof(t100_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k3_topreal1(np__2,k32_pscomp_1(A),k33_pscomp_1(A)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) )).

fof(t101_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r2_hidden(k32_pscomp_1(A),k27_pscomp_1(A))
        & r2_hidden(k33_pscomp_1(A),k27_pscomp_1(A)) ) ) )).

fof(t102_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_pscomp_1(A),k32_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k32_pscomp_1(A))
        & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k33_pscomp_1(A),k24_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k33_pscomp_1(A)) ) ) )).

fof(t103_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k32_pscomp_1(A) = k33_pscomp_1(A)
       => k27_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k32_pscomp_1(A)) ) ) )).

fof(t104_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k35_pscomp_1(A)) = k20_pscomp_1(A)
        & k21_euclid(k34_pscomp_1(A)) = k20_pscomp_1(A) ) ) )).

fof(t105_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k25_pscomp_1(A)) = k21_euclid(k35_pscomp_1(A))
        & k21_euclid(k25_pscomp_1(A)) = k21_euclid(k34_pscomp_1(A))
        & k21_euclid(k35_pscomp_1(A)) = k21_euclid(k34_pscomp_1(A))
        & k21_euclid(k35_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A))
        & k21_euclid(k34_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A)) ) ) )).

fof(t106_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k35_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))
        & k22_euclid(k34_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1)) ) ) )).

fof(t107_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k35_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k34_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k24_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k35_pscomp_1(A)),k22_euclid(k34_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k35_pscomp_1(A)),k22_euclid(k24_pscomp_1(A)))
        & r1_xreal_0(k22_euclid(k34_pscomp_1(A)),k22_euclid(k24_pscomp_1(A))) ) ) )).

fof(t108_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k28_pscomp_1(B))
           => ( k21_euclid(A) = k21_euclid(k35_pscomp_1(B))
              & ( v6_compts_1(B,k15_euclid(np__2))
               => ( r1_xreal_0(k22_euclid(k35_pscomp_1(B)),k22_euclid(A))
                  & r1_xreal_0(k22_euclid(A),k22_euclid(k34_pscomp_1(B))) ) ) ) ) ) ) )).

fof(t109_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k28_pscomp_1(A),k3_topreal1(np__2,k35_pscomp_1(A),k34_pscomp_1(A))) ) )).

fof(t110_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k3_topreal1(np__2,k35_pscomp_1(A),k34_pscomp_1(A)),k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A))) ) )).

fof(t111_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r2_hidden(k35_pscomp_1(A),k28_pscomp_1(A))
        & r2_hidden(k34_pscomp_1(A),k28_pscomp_1(A)) ) ) )).

fof(t112_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k25_pscomp_1(A),k35_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k35_pscomp_1(A))
        & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k34_pscomp_1(A),k24_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k34_pscomp_1(A)) ) ) )).

fof(t113_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k35_pscomp_1(A) = k34_pscomp_1(A)
       => k28_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k35_pscomp_1(A)) ) ) )).

fof(t114_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k37_pscomp_1(A)) = k21_pscomp_1(A)
        & k22_euclid(k36_pscomp_1(A)) = k21_pscomp_1(A) ) ) )).

fof(t115_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k22_euclid(k22_pscomp_1(A)) = k22_euclid(k37_pscomp_1(A))
        & k22_euclid(k22_pscomp_1(A)) = k22_euclid(k36_pscomp_1(A))
        & k22_euclid(k37_pscomp_1(A)) = k22_euclid(k36_pscomp_1(A))
        & k22_euclid(k37_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A))
        & k22_euclid(k36_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A)) ) ) )).

fof(t116_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k21_euclid(k37_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1))
        & k21_euclid(k36_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)) ) ) )).

fof(t117_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k37_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k36_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k25_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k37_pscomp_1(A)),k21_euclid(k36_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k37_pscomp_1(A)),k21_euclid(k25_pscomp_1(A)))
        & r1_xreal_0(k21_euclid(k36_pscomp_1(A)),k21_euclid(k25_pscomp_1(A))) ) ) )).

fof(t118_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
         => ( r2_hidden(A,k29_pscomp_1(B))
           => ( k22_euclid(A) = k22_euclid(k37_pscomp_1(B))
              & ( v6_compts_1(B,k15_euclid(np__2))
               => ( r1_xreal_0(k21_euclid(k37_pscomp_1(B)),k21_euclid(A))
                  & r1_xreal_0(k21_euclid(A),k21_euclid(k36_pscomp_1(B))) ) ) ) ) ) ) )).

fof(t119_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k29_pscomp_1(A),k3_topreal1(np__2,k37_pscomp_1(A),k36_pscomp_1(A))) ) )).

fof(t120_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => r1_tarski(k3_topreal1(np__2,k37_pscomp_1(A),k36_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A))) ) )).

fof(t121_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( r2_hidden(k37_pscomp_1(A),k29_pscomp_1(A))
        & r2_hidden(k36_pscomp_1(A),k29_pscomp_1(A)) ) ) )).

fof(t122_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k37_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k37_pscomp_1(A))
        & k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k36_pscomp_1(A),k25_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k36_pscomp_1(A)) ) ) )).

fof(t123_pscomp_1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v6_compts_1(A,k15_euclid(np__2))
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
     => ( k37_pscomp_1(A) = k36_pscomp_1(A)
       => k29_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k37_pscomp_1(A)) ) ) )).

fof(t124_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k31_pscomp_1(A) = k32_pscomp_1(A)
       => k31_pscomp_1(A) = k23_pscomp_1(A) ) ) )).

fof(t125_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k33_pscomp_1(A) = k34_pscomp_1(A)
       => k33_pscomp_1(A) = k24_pscomp_1(A) ) ) )).

fof(t126_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k35_pscomp_1(A) = k36_pscomp_1(A)
       => k35_pscomp_1(A) = k25_pscomp_1(A) ) ) )).

fof(t127_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ( k37_pscomp_1(A) = k30_pscomp_1(A)
       => k37_pscomp_1(A) = k22_pscomp_1(A) ) ) )).

fof(s1_pscomp_1,axiom,
    ( ! [A] :
        ~ ( r2_hidden(A,u1_struct_0(f1_s1_pscomp_1))
          & ! [B] :
              ( m1_subset_1(B,k1_numbers)
             => ~ p1_s1_pscomp_1(A,B) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(f1_s1_pscomp_1),k1_numbers)
        & m2_relset_1(A,u1_struct_0(f1_s1_pscomp_1),k1_numbers)
        & ! [B] :
            ( m1_subset_1(B,u1_struct_0(f1_s1_pscomp_1))
           => p1_s1_pscomp_1(B,k2_seq_1(u1_struct_0(f1_s1_pscomp_1),k1_numbers,A,B)) ) ) )).

fof(redefinition_v5_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v5_pscomp_1(B,A)
      <=> v2_seq_2(B) ) ) )).

fof(redefinition_v6_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v6_pscomp_1(B,A)
      <=> v1_seq_2(B) ) ) )).

fof(dt_k1_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) )).

fof(redefinition_k1_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k1_pscomp_1(A,B,C) = k2_relat_1(C) ) )).

fof(dt_k2_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_pscomp_1(A,B,C))
        & v1_funct_2(k2_pscomp_1(A,B,C),k1_pcomps_1(B),k1_pcomps_1(A))
        & m2_relset_1(k2_pscomp_1(A,B,C),k1_pcomps_1(B),k1_pcomps_1(A)) ) ) )).

fof(dt_k3_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k3_pscomp_1(A),k1_numbers) ) )).

fof(redefinition_k3_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k3_pscomp_1(A) = k2_seq_4(A) ) )).

fof(dt_k4_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k4_pscomp_1(A),k1_numbers) ) )).

fof(redefinition_k4_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k4_pscomp_1(A) = k3_seq_4(A) ) )).

fof(dt_k5_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k5_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(involutiveness_k5_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k5_pscomp_1(k5_pscomp_1(A)) = A ) )).

fof(dt_k6_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k6_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(dt_k7_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => m1_subset_1(k7_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) )).

fof(projectivity_k7_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k7_pscomp_1(k7_pscomp_1(A)) = k7_pscomp_1(A) ) )).

fof(dt_k8_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k8_pscomp_1(A,B))
        & v1_funct_2(k8_pscomp_1(A,B),A,k1_numbers)
        & m2_relset_1(k8_pscomp_1(A,B),A,k1_numbers) ) ) )).

fof(involutiveness_k8_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => k8_pscomp_1(A,k8_pscomp_1(A,B)) = B ) )).

fof(dt_k9_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_numbers)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k1_numbers)
        & m1_relset_1(C,A,k1_numbers) )
     => ( v1_funct_1(k9_pscomp_1(A,B,C))
        & v1_funct_2(k9_pscomp_1(A,B,C),A,k1_numbers)
        & m2_relset_1(k9_pscomp_1(A,B,C),A,k1_numbers) ) ) )).

fof(dt_k10_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => ( v1_funct_1(k10_pscomp_1(A,B))
        & v1_funct_2(k10_pscomp_1(A,B),A,k1_numbers)
        & m2_relset_1(k10_pscomp_1(A,B),A,k1_numbers) ) ) )).

fof(involutiveness_k10_pscomp_1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k1_numbers)
        & m1_relset_1(B,A,k1_numbers) )
     => k10_pscomp_1(A,k10_pscomp_1(A,B)) = B ) )).

fof(dt_k11_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => m1_subset_1(k11_pscomp_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(redefinition_k11_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => k11_pscomp_1(A,B,C) = k10_relat_1(B,C) ) )).

fof(dt_k12_pscomp_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => m1_subset_1(k12_pscomp_1(A,B),k1_numbers) ) )).

fof(dt_k13_pscomp_1,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),k1_numbers)
        & m1_relset_1(B,u1_struct_0(A),k1_numbers) )
     => m1_subset_1(k13_pscomp_1(A,B),k1_numbers) ) )).

fof(dt_k14_pscomp_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => m1_subset_1(k14_pscomp_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) )).

fof(redefinition_k14_pscomp_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
        & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => k14_pscomp_1(A,B,C,D) = k9_relat_1(C,D) ) )).

fof(dt_k15_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),k1_numbers)
        & m1_relset_1(C,u1_struct_0(A),k1_numbers) )
     => ( v1_funct_1(k15_pscomp_1(A,B,C))
        & v1_funct_2(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers)
        & m2_relset_1(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) ) ) )).

fof(dt_k16_pscomp_1,axiom,
    ( v1_funct_1(k16_pscomp_1)
    & v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & m2_relset_1(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers) )).

fof(dt_k17_pscomp_1,axiom,
    ( v1_funct_1(k17_pscomp_1)
    & v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
    & m2_relset_1(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers) )).

fof(dt_k18_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) )).

fof(dt_k19_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) )).

fof(dt_k20_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k20_pscomp_1(A),k1_numbers) ) )).

fof(dt_k21_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k21_pscomp_1(A),k1_numbers) ) )).

fof(dt_k22_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k22_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k23_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k23_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k24_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k24_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k25_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k25_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k26_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k26_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k27_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k27_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k28_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k28_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k29_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k29_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) )).

fof(dt_k30_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k30_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k31_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k31_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k32_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k32_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k33_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k33_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k34_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k34_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k35_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k35_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k36_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k36_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(dt_k37_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => m1_subset_1(k37_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) )).

fof(d7_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k5_pscomp_1(A) = a_1_0_pscomp_1(A) ) )).

fof(d8_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => k8_measure6(A,B) = a_2_0_pscomp_1(A,B) ) ) )).

fof(d9_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k6_pscomp_1(A) = a_1_1_pscomp_1(A) ) )).

fof(d10_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => k7_pscomp_1(A) = k1_setfam_1(a_1_2_pscomp_1(A)) ) )).

fof(t65_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k11_pscomp_1(k15_euclid(np__2),k16_pscomp_1,k2_rcomp_1(A,B)) = a_2_1_pscomp_1(A,B) ) ) )).

fof(t66_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( A = a_2_2_pscomp_1(B,C)
               => v3_pre_topc(A,k15_euclid(np__2)) ) ) ) ) )).

fof(t67_pscomp_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k11_pscomp_1(k15_euclid(np__2),k17_pscomp_1,k2_rcomp_1(A,B)) = a_2_3_pscomp_1(A,B) ) ) )).

fof(t68_pscomp_1,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( m1_subset_1(C,k1_numbers)
             => ( A = a_2_4_pscomp_1(B,C)
               => v3_pre_topc(A,k15_euclid(np__2)) ) ) ) ) )).

fof(fraenkel_a_1_0_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ( r2_hidden(A,a_1_0_pscomp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = k1_real_1(C)
            & r2_hidden(C,B) ) ) ) )).

fof(fraenkel_a_2_0_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_0_pscomp_1(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,k1_numbers)
            & A = k3_real_1(C,D)
            & r2_hidden(D,B) ) ) ) )).

fof(fraenkel_a_1_1_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ( r2_hidden(A,a_1_1_pscomp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_numbers)
            & A = k6_real_1(np__1,C)
            & r2_hidden(C,B) ) ) ) )).

fof(fraenkel_a_1_2_pscomp_1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ( r2_hidden(A,a_1_2_pscomp_1(B))
      <=> ? [C] :
            ( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
            & A = C
            & r1_tarski(B,C)
            & v2_rcomp_1(C) ) ) ) )).

fof(fraenkel_a_2_1_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_1_pscomp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_numbers)
            & m1_subset_1(E,k1_numbers)
            & A = k23_euclid(D,E)
            & ~ r1_xreal_0(D,B)
            & ~ r1_xreal_0(C,D) ) ) ) )).

fof(fraenkel_a_2_2_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_2_pscomp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_numbers)
            & m1_subset_1(E,k1_numbers)
            & A = k23_euclid(D,E)
            & ~ r1_xreal_0(D,B)
            & ~ r1_xreal_0(C,D) ) ) ) )).

fof(fraenkel_a_2_3_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( r2_hidden(A,a_2_3_pscomp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_numbers)
            & m1_subset_1(E,k1_numbers)
            & A = k23_euclid(D,E)
            & ~ r1_xreal_0(E,B)
            & ~ r1_xreal_0(C,E) ) ) ) )).

fof(fraenkel_a_2_4_pscomp_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => ( r2_hidden(A,a_2_4_pscomp_1(B,C))
      <=> ? [D,E] :
            ( m1_subset_1(D,k1_numbers)
            & m1_subset_1(E,k1_numbers)
            & A = k23_euclid(D,E)
            & ~ r1_xreal_0(E,B)
            & ~ r1_xreal_0(C,E) ) ) ) )).
%------------------------------------------------------------------------------