SET007 Axioms: SET007+175.ax


%------------------------------------------------------------------------------
% File     : SET007+175 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Properties of the Intervals
% 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    : measure6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   84 (  10 unit)
%            Number of atoms       :  520 (  75 equality)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives :  532 (  96 ~  ;  16  |; 183  &)
%                                         (  12 <=>; 225 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (  11 constant; 0-3 arity)
%            Number of variables   :  183 (   0 singleton; 179 !;   4 ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_measure6,axiom,(
    ! [A,B] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
        & v1_xreal_0(B) )
     => ( v5_measure5(k8_measure6(A,B))
        & v1_membered(k8_measure6(A,B))
        & v2_membered(k8_measure6(A,B)) ) ) )).

fof(t1_measure6,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,k5_numbers,k2_zfmisc_1(k5_numbers,k5_numbers))
      & m2_relset_1(A,k5_numbers,k2_zfmisc_1(k5_numbers,k5_numbers))
      & v2_funct_1(A)
      & k1_relat_1(A) = k5_numbers
      & k2_relat_1(A) = k2_zfmisc_1(k5_numbers,k5_numbers) ) )).

fof(t2_measure6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => r1_supinf_1(k1_supinf_2,k19_supinf_2(A)) ) ) )).

fof(t3_measure6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( v6_supinf_2(A,k5_numbers)
           => ( ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ r1_supinf_1(B,k13_supinf_2(A,C)) )
              | r1_supinf_1(B,k19_supinf_2(A)) ) ) ) ) )).

fof(t4_measure6,axiom,(
    $true )).

fof(t5_measure6,axiom,(
    $true )).

fof(t6_measure6,axiom,(
    $true )).

fof(t7_measure6,axiom,(
    $true )).

fof(t8_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( m1_subset_1(A,k1_numbers)
           => ( k2_supinf_2(k4_supinf_2(B,A),A) = B
              & k4_supinf_2(k2_supinf_2(B,A),A) = B ) ) ) ) )).

fof(t9_measure6,axiom,(
    $true )).

fof(t10_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( r2_hidden(C,k6_supinf_1)
               => ( r1_supinf_1(A,B)
                  | k4_supinf_2(k2_supinf_2(C,A),k2_supinf_2(C,B)) = k4_supinf_2(A,B) ) ) ) ) ) )).

fof(t11_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r2_hidden(C,k6_supinf_1)
                  & r1_supinf_1(A,B) )
               => ( r1_supinf_1(k2_supinf_2(C,A),k2_supinf_2(C,B))
                  & r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,C))
                  & r1_supinf_1(k4_supinf_2(A,C),k4_supinf_2(B,C)) ) ) ) ) ) )).

fof(t12_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( r2_hidden(C,k6_supinf_1)
               => ( r1_supinf_1(B,A)
                  | ( ~ r1_supinf_1(k2_supinf_2(C,B),k2_supinf_2(C,A))
                    & ~ r1_supinf_1(k2_supinf_2(B,C),k2_supinf_2(A,C))
                    & ~ r1_supinf_1(k4_supinf_2(B,C),k4_supinf_2(A,C)) ) ) ) ) ) ) )).

fof(d1_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k1_measure6(A) = A ) )).

fof(t13_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> r1_supinf_1(k1_measure6(A),k1_measure6(B)) ) ) ) )).

fof(t14_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ ( ~ r1_xreal_0(B,A)
                & r1_supinf_1(k1_measure6(B),k1_measure6(A)) )
            & ~ ( ~ r1_supinf_1(k1_measure6(B),k1_measure6(A))
                & r1_xreal_0(B,A) ) ) ) ) )).

fof(t15_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ~ ( ~ r1_supinf_1(B,A)
                  & ~ r1_supinf_1(C,B)
                  & ~ m1_subset_1(B,k1_numbers) ) ) ) ) )).

fof(t16_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( m1_subset_1(A,k1_numbers)
                  & m1_subset_1(C,k1_numbers)
                  & r1_supinf_1(A,B)
                  & r1_supinf_1(B,C) )
               => m1_subset_1(B,k1_numbers) ) ) ) ) )).

fof(t17_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( m1_subset_1(A,k1_numbers)
                  & r1_supinf_1(A,B) )
               => ( r1_supinf_1(C,B)
                  | m1_subset_1(B,k1_numbers) ) ) ) ) ) )).

fof(t18_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(B,C)
                  & m1_subset_1(C,k1_numbers) )
               => ( r1_supinf_1(B,A)
                  | m1_subset_1(B,k1_numbers) ) ) ) ) ) )).

fof(t19_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
              & ~ r1_supinf_1(B,A)
              & r1_supinf_1(k4_supinf_2(B,A),k1_supinf_2) ) ) ) )).

fof(t20_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ~ ( r1_supinf_1(k1_supinf_2,A)
                  & r1_supinf_1(k1_supinf_2,C)
                  & ~ r1_supinf_1(B,k2_supinf_2(C,A))
                  & r1_supinf_1(k4_supinf_2(B,A),C) ) ) ) ) )).

fof(t21_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k4_supinf_2(A,k1_supinf_2) = A ) )).

fof(t22_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(k1_supinf_2,A)
                  & r1_supinf_1(k1_supinf_2,C) )
               => ( r1_supinf_1(B,k2_supinf_2(C,A))
                  | r1_supinf_1(C,B) ) ) ) ) ) )).

fof(t23_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( ~ r1_supinf_1(B,k1_supinf_2)
                  & ~ r1_supinf_1(A,B) ) ) ) ) )).

fof(t24_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
              & ~ r1_supinf_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( ~ r1_supinf_1(C,k1_supinf_2)
                      & ~ r1_supinf_1(B,k2_supinf_2(A,C))
                      & r2_hidden(C,k6_supinf_1) ) ) ) ) ) )).

fof(t25_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( r1_supinf_1(k1_supinf_2,A)
              & ~ r1_supinf_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( ~ r1_supinf_1(C,k1_supinf_2)
                      & ~ r1_supinf_1(B,k2_supinf_2(A,C))
                      & r2_hidden(C,k6_supinf_1) ) ) ) ) ) )).

fof(t26_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
          & ! [B] :
              ( m1_subset_1(B,k3_supinf_1)
             => ~ ( ~ r1_supinf_1(B,k1_supinf_2)
                  & ~ r1_supinf_1(A,k2_supinf_2(B,B)) ) ) ) ) )).

fof(d2_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ r1_supinf_1(A,k1_supinf_2)
       => ! [B] :
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
           => ( B = k2_measure6(A)
            <=> ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( r2_hidden(C,B)
                  <=> ( ~ r1_supinf_1(C,k1_supinf_2)
                      & ~ r1_supinf_1(A,k2_supinf_2(C,C)) ) ) ) ) ) ) ) )).

fof(d3_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => k3_measure6(A) = k9_supinf_1(k2_measure6(A)) ) )).

fof(t27_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
          & r1_supinf_1(k3_measure6(A),k1_supinf_2) ) ) )).

fof(t28_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ r1_supinf_1(A,k1_supinf_2)
       => r1_supinf_1(k3_measure6(A),A) ) ) )).

fof(t29_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
          & ~ r1_supinf_1(k4_supinf_1,A)
          & ~ m1_subset_1(k3_measure6(A),k1_numbers) ) ) )).

fof(t30_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ r1_supinf_1(A,k1_supinf_2)
       => r1_supinf_1(k2_supinf_2(k3_measure6(A),k3_measure6(A)),A) ) ) )).

fof(t31_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
          & ! [B] :
              ( ( v1_funct_1(B)
                & v1_funct_2(B,k5_numbers,k3_supinf_1)
                & m2_relset_1(B,k5_numbers,k3_supinf_1) )
             => ~ ( ! [C] :
                      ( m2_subset_1(C,k1_numbers,k5_numbers)
                     => ~ r1_supinf_1(k13_supinf_2(B,C),k1_supinf_2) )
                  & ~ r1_supinf_1(A,k19_supinf_2(B)) ) ) ) ) )).

fof(t32_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
              & m1_subset_1(k10_supinf_1(B),k1_numbers)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( r2_hidden(C,B)
                      & ~ r1_supinf_1(k2_supinf_2(k10_supinf_1(B),A),C) ) ) ) ) ) )).

fof(t33_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k3_supinf_1)) )
         => ~ ( ~ r1_supinf_1(A,k1_supinf_2)
              & m1_subset_1(k9_supinf_1(B),k1_numbers)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( r2_hidden(C,B)
                      & ~ r1_supinf_1(C,k4_supinf_2(k9_supinf_1(B),A)) ) ) ) ) ) )).

fof(t34_measure6,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k3_supinf_1)
        & m2_relset_1(A,k5_numbers,k3_supinf_1) )
     => ( v6_supinf_2(A,k5_numbers)
       => ( r1_supinf_1(k4_supinf_1,k19_supinf_2(A))
          | ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => r2_hidden(k13_supinf_2(A,B),k6_supinf_1) ) ) ) ) )).

fof(t35_measure6,axiom,
    ( v5_measure5(k6_supinf_1)
    & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k6_supinf_1))
    & k6_supinf_1 = k2_measure5(k4_measure6,k5_measure6)
    & k6_supinf_1 = k1_measure5(k4_measure6,k5_measure6)
    & k6_supinf_1 = k4_measure5(k4_measure6,k5_measure6)
    & k6_supinf_1 = k3_measure5(k4_measure6,k5_measure6) )).

fof(t36_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( B = k4_measure6
           => ( k2_measure5(A,B) = k6_measure5
              & k1_measure5(A,B) = k6_measure5
              & k4_measure5(A,B) = k6_measure5
              & k3_measure5(A,B) = k6_measure5 ) ) ) ) )).

fof(t37_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( A = k5_measure6
           => ( k2_measure5(A,B) = k6_measure5
              & k1_measure5(A,B) = k6_measure5
              & k4_measure5(A,B) = k6_measure5
              & k3_measure5(A,B) = k6_measure5 ) ) ) ) )).

fof(t38_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( ( A = k2_measure5(B,C)
                              & r2_hidden(D,A)
                              & r2_hidden(E,A)
                              & r1_xreal_0(D,F)
                              & r1_xreal_0(F,E) )
                           => r2_hidden(F,A) ) ) ) ) ) ) ) )).

fof(t39_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( ( A = k1_measure5(B,C)
                              & r2_hidden(D,A)
                              & r2_hidden(E,A)
                              & r1_xreal_0(D,F)
                              & r1_xreal_0(F,E) )
                           => r2_hidden(F,A) ) ) ) ) ) ) ) )).

fof(t40_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( ( A = k3_measure5(B,C)
                              & r2_hidden(D,A)
                              & r2_hidden(E,A)
                              & r1_xreal_0(D,F)
                              & r1_xreal_0(F,E) )
                           => r2_hidden(F,A) ) ) ) ) ) ) ) )).

fof(t41_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] :
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] :
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ( ( A = k4_measure5(B,C)
                              & r2_hidden(D,A)
                              & r2_hidden(E,A)
                              & r1_xreal_0(D,F)
                              & r1_xreal_0(F,E) )
                           => r2_hidden(F,A) ) ) ) ) ) ) ) )).

fof(t42_measure6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( B = k10_supinf_1(A)
                  & C = k9_supinf_1(A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( ( r2_hidden(D,A)
                              & r2_hidden(E,A) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( ( r1_xreal_0(D,F)
                                    & r1_xreal_0(F,E) )
                                 => r2_hidden(F,A) ) ) ) ) ) )
               => ( r2_hidden(B,A)
                  | r2_hidden(C,A)
                  | A = k2_measure5(B,C) ) ) ) ) ) )).

fof(t43_measure6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( B = k10_supinf_1(A)
                  & C = k9_supinf_1(A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( ( r2_hidden(D,A)
                              & r2_hidden(E,A) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( ( r1_xreal_0(D,F)
                                    & r1_xreal_0(F,E) )
                                 => r2_hidden(F,A) ) ) ) ) )
                  & r2_hidden(B,A)
                  & r2_hidden(C,A)
                  & r1_tarski(A,k6_supinf_1) )
               => A = k1_measure5(B,C) ) ) ) ) )).

fof(t44_measure6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( B = k10_supinf_1(A)
                  & C = k9_supinf_1(A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( ( r2_hidden(D,A)
                              & r2_hidden(E,A) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( ( r1_xreal_0(D,F)
                                    & r1_xreal_0(F,E) )
                                 => r2_hidden(F,A) ) ) ) ) )
                  & r2_hidden(B,A)
                  & r1_tarski(A,k6_supinf_1) )
               => ( r2_hidden(C,A)
                  | A = k4_measure5(B,C) ) ) ) ) ) )).

fof(t45_measure6,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( B = k10_supinf_1(A)
                  & C = k9_supinf_1(A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ( ( r2_hidden(D,A)
                              & r2_hidden(E,A) )
                           => ! [F] :
                                ( m1_subset_1(F,k1_numbers)
                               => ( ( r1_xreal_0(D,F)
                                    & r1_xreal_0(F,E) )
                                 => r2_hidden(F,A) ) ) ) ) )
                  & r2_hidden(C,A)
                  & r1_tarski(A,k6_supinf_1) )
               => ( r2_hidden(B,A)
                  | A = k3_measure5(B,C) ) ) ) ) ) )).

fof(t46_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( ( v5_measure5(A)
          & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => ( ( r1_xreal_0(B,D)
                          & r1_xreal_0(D,C) )
                       => r2_hidden(D,A) ) ) ) ) ) ) ) )).

fof(t47_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( ( v5_measure5(B)
            & m1_subset_1(B,k1_zfmisc_1(k6_supinf_1)) )
         => ( ~ r1_xboole_0(A,B)
           => ( v5_measure5(k4_subset_1(k6_supinf_1,A,B))
              & m1_subset_1(k4_subset_1(k6_supinf_1,A,B),k1_zfmisc_1(k6_supinf_1)) ) ) ) ) )).

fof(d4_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( A != k6_measure5
       => ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( B = k6_measure6(A)
            <=> ? [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                  & r1_supinf_1(B,C)
                  & ~ ( A != k2_measure5(B,C)
                      & A != k3_measure5(B,C)
                      & A != k1_measure5(B,C)
                      & A != k4_measure5(B,C) ) ) ) ) ) ) )).

fof(d5_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( A != k6_measure5
       => ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ( B = k7_measure6(A)
            <=> ? [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                  & r1_supinf_1(C,B)
                  & ~ ( A != k2_measure5(C,B)
                      & A != k3_measure5(C,B)
                      & A != k1_measure5(C,B)
                      & A != k4_measure5(C,B) ) ) ) ) ) ) )).

fof(t48_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( v1_measure5(A)
       => ( A = k6_measure5
          | ( r1_supinf_1(k6_measure6(A),k7_measure6(A))
            & A = k2_measure5(k6_measure6(A),k7_measure6(A)) ) ) ) ) )).

fof(t49_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( v2_measure5(A)
       => ( A = k6_measure5
          | ( r1_supinf_1(k6_measure6(A),k7_measure6(A))
            & A = k1_measure5(k6_measure6(A),k7_measure6(A)) ) ) ) ) )).

fof(t50_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( v3_measure5(A)
       => ( A = k6_measure5
          | ( r1_supinf_1(k6_measure6(A),k7_measure6(A))
            & A = k4_measure5(k6_measure6(A),k7_measure6(A)) ) ) ) ) )).

fof(t51_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( v4_measure5(A)
       => ( A = k6_measure5
          | ( r1_supinf_1(k6_measure6(A),k7_measure6(A))
            & A = k3_measure5(k6_measure6(A),k7_measure6(A)) ) ) ) ) )).

fof(t52_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( A != k6_measure5
       => ( r1_supinf_1(k6_measure6(A),k7_measure6(A))
          & ~ ( A != k2_measure5(k6_measure6(A),k7_measure6(A))
              & A != k3_measure5(k6_measure6(A),k7_measure6(A))
              & A != k1_measure5(k6_measure6(A),k7_measure6(A))
              & A != k4_measure5(k6_measure6(A),k7_measure6(A)) ) ) ) ) )).

fof(t53_measure6,axiom,(
    $true )).

fof(t54_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r2_hidden(B,A)
           => ( r1_supinf_1(k6_measure6(A),k1_measure6(B))
              & r1_supinf_1(k1_measure6(B),k7_measure6(A)) ) ) ) ) )).

fof(t55_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( ( v5_measure5(B)
            & m1_subset_1(B,k1_zfmisc_1(k6_supinf_1)) )
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r2_hidden(C,A)
                      & r2_hidden(D,B)
                      & r1_supinf_1(k7_measure6(A),k6_measure6(B)) )
                   => r1_xreal_0(C,D) ) ) ) ) ) )).

fof(t56_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r2_hidden(B,A)
           => ( r1_supinf_1(k6_measure6(A),B)
              & r1_supinf_1(B,k7_measure6(A)) ) ) ) ) )).

fof(t57_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ( A != k6_measure5
       => ! [B] :
            ( m1_subset_1(B,k3_supinf_1)
           => ~ ( ~ r1_supinf_1(B,k6_measure6(A))
                & ~ r1_supinf_1(k7_measure6(A),B)
                & ~ r2_hidden(B,A) ) ) ) ) )).

fof(t58_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( ( v5_measure5(B)
            & m1_subset_1(B,k1_zfmisc_1(k6_supinf_1)) )
         => ( k7_measure6(A) = k6_measure6(B)
           => ( ( ~ r2_hidden(k7_measure6(A),A)
                & ~ r2_hidden(k6_measure6(B),B) )
              | ( v5_measure5(k4_subset_1(k6_supinf_1,A,B))
                & m1_subset_1(k4_subset_1(k6_supinf_1,A,B),k1_zfmisc_1(k6_supinf_1)) ) ) ) ) ) )).

fof(d6_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k6_supinf_1))
             => ( C = k8_measure6(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k1_numbers)
                   => ( r2_hidden(D,C)
                    <=> ? [E] :
                          ( m1_subset_1(E,k1_numbers)
                          & r2_hidden(E,A)
                          & D = k2_xcmplx_0(B,E) ) ) ) ) ) ) ) )).

fof(t59_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ! [B] :
          ( v1_xreal_0(B)
         => k8_measure6(k8_measure6(A,B),k4_xcmplx_0(B)) = A ) ) )).

fof(t60_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k6_supinf_1))
         => ( B = k6_supinf_1
           => k8_measure6(B,A) = B ) ) ) )).

fof(t61_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k8_measure6(k6_measure5,A) = k6_measure5 ) )).

fof(t62_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v1_measure5(A)
          <=> v1_measure5(k8_measure6(A,B)) ) ) ) )).

fof(t63_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v2_measure5(A)
          <=> v2_measure5(k8_measure6(A,B)) ) ) ) )).

fof(t64_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v3_measure5(A)
          <=> v3_measure5(k8_measure6(A,B)) ) ) ) )).

fof(t65_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v4_measure5(A)
          <=> v4_measure5(k8_measure6(A,B)) ) ) ) )).

fof(t66_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => ( v5_measure5(k8_measure6(A,B))
            & m1_subset_1(k8_measure6(A,B),k1_zfmisc_1(k6_supinf_1)) ) ) ) )).

fof(t67_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( v1_xreal_0(B)
         => k5_measure5(A) = k5_measure5(k8_measure6(A,B)) ) ) )).

fof(dt_k1_measure6,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => m1_subset_1(k1_measure6(A),k3_supinf_1) ) )).

fof(dt_k2_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ v1_xboole_0(k2_measure6(A))
        & m1_subset_1(k2_measure6(A),k1_zfmisc_1(k3_supinf_1)) ) ) )).

fof(dt_k3_measure6,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k3_measure6(A),k3_supinf_1) ) )).

fof(dt_k4_measure6,axiom,(
    m1_subset_1(k4_measure6,k3_supinf_1) )).

fof(redefinition_k4_measure6,axiom,(
    k4_measure6 = k2_supinf_1 )).

fof(dt_k5_measure6,axiom,(
    m1_subset_1(k5_measure6,k3_supinf_1) )).

fof(redefinition_k5_measure6,axiom,(
    k5_measure6 = k1_supinf_1 )).

fof(dt_k6_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => m1_subset_1(k6_measure6(A),k3_supinf_1) ) )).

fof(dt_k7_measure6,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => m1_subset_1(k7_measure6(A),k3_supinf_1) ) )).

fof(dt_k8_measure6,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
        & v1_xreal_0(B) )
     => m1_subset_1(k8_measure6(A,B),k1_zfmisc_1(k6_supinf_1)) ) )).
%------------------------------------------------------------------------------