SET007 Axioms: SET007+155.ax


%------------------------------------------------------------------------------
% File     : SET007+155 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The sigma-additive Measure Theory
% 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    : measure1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  116 (  27 unit)
%            Number of atoms       :  717 (  54 equality)
%            Maximal formula depth :   19 (   8 average)
%            Number of connectives :  695 (  94 ~  ;   3  |; 371  &)
%                                         (  13 <=>; 214 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   29 (   1 propositional; 0-4 arity)
%            Number of functors    :   35 (   9 constant; 0-5 arity)
%            Number of variables   :  333 (   0 singleton; 313 !;  20 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ~ v1_xboole_0(k7_setfam_1(A,B)) ) )).

fof(cc1_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v1_finsub_1(B)
          & v1_prob_1(B,A) )
       => v2_finsub_1(B) ) ) )).

fof(cc2_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v2_finsub_1(B)
          & v1_prob_1(B,A) )
       => v1_finsub_1(B) ) ) )).

fof(rc1_measure1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finsub_1(B)
      & v2_finsub_1(B)
      & v1_prob_1(B,A) ) )).

fof(rc2_measure1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_card_4(B) ) )).

fof(rc3_measure1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_prob_1(B,A)
      & v1_measure1(B,A) ) )).

fof(cc3_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) ) ) ) )).

fof(rc4_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] :
          ( m1_relset_1(C,k5_numbers,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,k5_numbers,B)
          & v1_prob_2(C) ) ) )).

fof(cc4_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A) )
       => ( ~ v1_xboole_0(B)
          & v1_finsub_1(B) ) ) ) )).

fof(t1_measure1,axiom,(
    ! [A,B] : k3_tarski(k1_enumset1(A,B,k1_xboole_0)) = k3_tarski(k2_tarski(A,B)) )).

fof(t2_measure1,axiom,(
    $true )).

fof(t3_measure1,axiom,(
    $true )).

fof(t4_measure1,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)
             => ! [D] :
                  ( m1_subset_1(D,k3_supinf_1)
                 => ( ( r1_supinf_1(k1_supinf_2,A)
                      & r1_supinf_1(k1_supinf_2,C)
                      & r1_supinf_1(A,B)
                      & r1_supinf_1(C,D) )
                   => r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) )).

fof(t5_measure1,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,B)
                  & r1_supinf_1(k1_supinf_2,C)
                  & A = k2_supinf_2(B,C) )
               => ( r1_supinf_1(k4_supinf_1,B)
                  | C = k4_supinf_2(A,B) ) ) ) ) ) )).

fof(t6_measure1,axiom,(
    $true )).

fof(t7_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).

fof(t8_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ( ~ v1_xboole_0(k1_enumset1(B,C,D))
                & m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ) )).

fof(t9_measure1,axiom,(
    ! [A] : m1_subset_1(k1_tarski(k1_xboole_0),k1_zfmisc_1(k1_zfmisc_1(A))) )).

fof(t10_measure1,axiom,(
    $true )).

fof(t11_measure1,axiom,(
    $true )).

fof(t12_measure1,axiom,(
    $true )).

fof(t13_measure1,axiom,(
    $true )).

fof(t14_measure1,axiom,(
    $true )).

fof(t15_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( k6_setfam_1(A,B) = k4_xboole_0(A,k5_setfam_1(A,k7_setfam_1(A,B)))
        & k5_setfam_1(A,B) = k4_xboole_0(A,k6_setfam_1(A,k7_setfam_1(A,B))) ) ) )).

fof(d1_measure1,axiom,(
    $true )).

fof(d2_measure1,axiom,(
    $true )).

fof(d3_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_prob_1(B,A)
      <=> ! [C] :
            ( r2_hidden(C,B)
           => r2_hidden(k4_xboole_0(A,C),B) ) ) ) )).

fof(t16_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( v1_finsub_1(B)
          & v1_prob_1(B,A) )
       => v2_finsub_1(B) ) ) )).

fof(t17_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => B = k7_setfam_1(A,B) ) )).

fof(t18_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
    <=> ? [C] :
          ( ~ v1_xboole_0(C)
          & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
          & B = C
          & ! [D] :
              ( r2_hidden(D,C)
             => ( r2_hidden(k4_xboole_0(A,D),C)
                & ! [E,F] :
                    ( ( r2_hidden(E,C)
                      & r2_hidden(F,C) )
                   => r2_hidden(k2_xboole_0(E,F),C) ) ) ) ) ) )).

fof(t19_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ( ~ v1_xboole_0(B)
          & v2_finsub_1(B)
          & v1_prob_1(B,A)
          & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
      <=> ! [C] :
            ( r2_hidden(C,B)
           => ( r2_hidden(k4_xboole_0(A,C),B)
              & ! [D,E] :
                  ( ( r2_hidden(D,B)
                    & r2_hidden(E,B) )
                 => r2_hidden(k3_xboole_0(D,E),B) ) ) ) ) ) )).

fof(t20_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C,D] :
          ( ( r2_hidden(C,B)
            & r2_hidden(D,B) )
         => r2_hidden(k4_xboole_0(C,D),B) ) ) )).

fof(t21_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( r2_hidden(k1_xboole_0,B)
        & r2_hidden(A,B) ) ) )).

fof(d4_measure1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_supinf_1)
            & m2_relset_1(B,A,k3_supinf_1) )
         => ( v6_supinf_2(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => r1_supinf_1(k1_supinf_2,k1_measure1(A,B,C)) ) ) ) ) )).

fof(t22_measure1,axiom,(
    $true )).

fof(t23_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,B,k3_supinf_1)
          & m2_relset_1(C,B,k3_supinf_1)
          & v6_supinf_2(C,B)
          & k1_funct_1(C,k1_xboole_0) = k1_supinf_2
          & ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_xboole_0(D,E)
                   => k1_funct_1(C,k4_subset_1(A,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) )).

fof(d5_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) )
         => ( m1_measure1(C,A,B)
          <=> ( v6_supinf_2(C,B)
              & k1_funct_1(C,k1_xboole_0) = k1_supinf_2
              & ! [D] :
                  ( m2_subset_1(D,k1_zfmisc_1(A),B)
                 => ! [E] :
                      ( m2_subset_1(E,k1_zfmisc_1(A),B)
                     => ( r1_xboole_0(D,E)
                       => k1_funct_1(C,k4_subset_1(A,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) ) ) )).

fof(t24_measure1,axiom,(
    $true )).

fof(t25_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_tarski(D,E)
                   => r1_supinf_1(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) )).

fof(t26_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_tarski(D,E)
                   => ( r1_supinf_1(k4_supinf_1,k1_measure1(B,C,D))
                      | k1_funct_1(C,k6_subset_1(A,E,D)) = k4_supinf_2(k1_measure1(B,C,E),k1_measure1(B,C,D)) ) ) ) ) ) ) )).

fof(t27_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => r1_supinf_1(k1_measure1(B,C,k2_measure1(A,B,D,E)),k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E))) ) ) ) ) )).

fof(d6_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( r1_measure1(A,B,C,D)
            <=> r2_hidden(D,B) ) ) ) )).

fof(t28_measure1,axiom,(
    $true )).

fof(t29_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ( r1_measure1(A,B,C,k1_xboole_0)
            & r1_measure1(A,B,C,A)
            & ! [D,E] :
                ( ( r1_measure1(A,B,C,D)
                  & r1_measure1(A,B,C,E) )
               => ( r1_measure1(A,B,C,k4_xboole_0(A,D))
                  & r1_measure1(A,B,C,k2_xboole_0(D,E))
                  & r1_measure1(A,B,C,k3_xboole_0(D,E)) ) ) ) ) ) )).

fof(d7_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ( m2_measure1(D,A,B,C)
              <=> k1_measure1(B,C,D) = k1_supinf_2 ) ) ) ) )).

fof(t30_measure1,axiom,(
    $true )).

fof(t31_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_measure1(E,A,B,C)
                 => ( r1_tarski(D,E)
                   => m2_measure1(D,A,B,C) ) ) ) ) ) )).

fof(t32_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_measure1(D,A,B,C)
             => ! [E] :
                  ( m2_measure1(E,A,B,C)
                 => ( m2_measure1(k2_measure1(A,B,D,E),A,B,C)
                    & m2_measure1(k3_measure1(A,B,D,E),A,B,C)
                    & m2_measure1(k4_measure1(A,B,D,E),A,B,C) ) ) ) ) ) )).

fof(t33_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_measure1(E,A,B,C)
                 => ( k1_measure1(B,C,k2_measure1(A,B,D,E)) = k1_measure1(B,C,D)
                    & k1_measure1(B,C,k3_measure1(A,B,D,E)) = k1_supinf_2
                    & k1_measure1(B,C,k4_measure1(A,B,D,E)) = k1_measure1(B,C,D) ) ) ) ) ) )).

fof(t34_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,k5_numbers,k1_zfmisc_1(A))
          & m2_relset_1(C,k5_numbers,k1_zfmisc_1(A))
          & k2_relat_1(C) = k1_tarski(B) ) ) )).

fof(t35_measure1,axiom,(
    ! [A] :
    ? [B] :
      ( v1_funct_1(B)
      & v1_funct_2(B,k5_numbers,k1_tarski(A))
      & m2_relset_1(B,k5_numbers,k1_tarski(A))
      & ! [C] :
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => k8_funct_2(k5_numbers,k1_tarski(A),B,C) = A ) ) )).

fof(t36_measure1,axiom,(
    $true )).

fof(t37_measure1,axiom,(
    $true )).

fof(t38_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(A))
             => ? [E] :
                  ( v1_funct_1(E)
                  & v1_funct_2(E,k5_numbers,k1_zfmisc_1(A))
                  & m2_relset_1(E,k5_numbers,k1_zfmisc_1(A))
                  & k2_relat_1(E) = k1_enumset1(B,C,D)
                  & k1_prob_1(A,E,np__0) = B
                  & k1_prob_1(A,E,np__1) = C
                  & ! [F] :
                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                     => ( ~ r1_xreal_0(F,np__1)
                       => k1_prob_1(A,E,F) = D ) ) ) ) ) ) )).

fof(t39_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(k1_enumset1(B,C,k1_xboole_0))
            & v1_card_4(k1_enumset1(B,C,k1_xboole_0))
            & m1_subset_1(k1_enumset1(B,C,k1_xboole_0),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).

fof(t40_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ? [D] :
              ( v1_funct_1(D)
              & v1_funct_2(D,k5_numbers,k1_zfmisc_1(A))
              & m2_relset_1(D,k5_numbers,k1_zfmisc_1(A))
              & k2_relat_1(D) = k2_tarski(B,C)
              & k1_prob_1(A,D,np__0) = B
              & ! [E] :
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(E,np__0)
                   => k1_prob_1(A,D,E) = C ) ) ) ) ) )).

fof(t41_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(k2_tarski(B,C))
            & v1_card_4(k2_tarski(B,C))
            & m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).

fof(t42_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_card_4(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ~ v1_xboole_0(k7_setfam_1(A,B))
        & v1_card_4(k7_setfam_1(A,B))
        & m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).

fof(d8_measure1,axiom,(
    $true )).

fof(d9_measure1,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_measure1(B,A)
      <=> ! [C] :
            ( ( ~ v1_xboole_0(C)
              & v1_card_4(C)
              & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
           => ( r1_tarski(C,B)
             => r2_hidden(k5_setfam_1(A,C),B) ) ) ) ) )).

fof(t43_measure1,axiom,(
    $true )).

fof(t44_measure1,axiom,(
    $true )).

fof(t45_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( r2_hidden(k1_xboole_0,B)
        & r2_hidden(A,B) ) ) )).

fof(t46_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C,D] :
          ( ( r2_hidden(C,B)
            & r2_hidden(D,B) )
         => ( r2_hidden(k2_xboole_0(C,D),B)
            & r2_hidden(k3_xboole_0(C,D),B) ) ) ) )).

fof(t47_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C,D] :
          ( ( r2_hidden(C,B)
            & r2_hidden(D,B) )
         => r2_hidden(k4_xboole_0(C,D),B) ) ) )).

fof(t48_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => B = k7_setfam_1(A,B) ) )).

fof(t49_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ( ( ! [C] :
              ( r2_hidden(C,B)
             => r2_hidden(k4_xboole_0(A,C),B) )
          & ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_card_4(C)
                & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
             => ( r1_tarski(C,B)
               => r2_hidden(k6_setfam_1(A,C),B) ) ) )
      <=> ( ~ v1_xboole_0(B)
          & v1_prob_1(B,A)
          & v1_measure1(B,A)
          & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).

fof(t50_measure1,axiom,(
    $true )).

fof(t51_measure1,axiom,(
    $true )).

fof(t52_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,B)
            & m2_relset_1(C,k5_numbers,B) )
         => ( ~ v1_xboole_0(k5_measure1(A,B,C))
            & v1_card_4(k5_measure1(A,B,C))
            & m1_subset_1(k5_measure1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).

fof(t53_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,k5_numbers,B)
            & m2_relset_1(C,k5_numbers,B) )
         => m2_subset_1(k5_setfam_1(A,k5_measure1(A,B,C)),k1_zfmisc_1(A),B) ) ) )).

fof(t54_measure1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(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,B,k3_supinf_1)
                    & m2_relset_1(D,B,k3_supinf_1) )
                 => ( v6_supinf_2(D,B)
                   => v6_supinf_2(k7_funct_2(A,B,k3_supinf_1,C,D),A) ) ) ) ) ) )).

fof(t55_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_subset_1(C,k3_supinf_1)
         => ! [D] :
              ( m1_subset_1(D,k3_supinf_1)
             => ? [E] :
                  ( v1_funct_1(E)
                  & v1_funct_2(E,B,k3_supinf_1)
                  & m2_relset_1(E,B,k3_supinf_1)
                  & ! [F] :
                      ( m2_subset_1(F,k1_zfmisc_1(A),B)
                     => ( ( F = k1_xboole_0
                         => k1_measure1(B,E,F) = C )
                        & ( F != k1_xboole_0
                         => k1_measure1(B,E,F) = D ) ) ) ) ) ) ) )).

fof(t56_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,B,k3_supinf_1)
          & m2_relset_1(C,B,k3_supinf_1)
          & ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ( ( D = k1_xboole_0
                 => k1_measure1(B,C,D) = k1_supinf_2 )
                & ( D != k1_xboole_0
                 => k1_measure1(B,C,D) = k4_supinf_1 ) ) ) ) ) )).

fof(t57_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,B,k3_supinf_1)
          & m2_relset_1(C,B,k3_supinf_1)
          & ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => k1_measure1(B,C,D) = k1_supinf_2 ) ) ) )).

fof(t58_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] :
          ( v1_funct_1(C)
          & v1_funct_2(C,B,k3_supinf_1)
          & m2_relset_1(C,B,k3_supinf_1)
          & v6_supinf_2(C,B)
          & k1_funct_1(C,k1_xboole_0) = k1_supinf_2
          & ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k5_numbers,B)
                & v1_prob_2(D)
                & m2_relset_1(D,k5_numbers,B) )
             => k19_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)) = k1_funct_1(C,k5_setfam_1(A,k5_measure1(A,B,D))) ) ) ) )).

fof(d10_measure1,axiom,(
    $true )).

fof(d11_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) )
         => ( m3_measure1(C,A,B)
          <=> ( v6_supinf_2(C,B)
              & k1_funct_1(C,k1_xboole_0) = k1_supinf_2
              & ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,B)
                    & v1_prob_2(D)
                    & m2_relset_1(D,k5_numbers,B) )
                 => k19_supinf_2(k7_funct_2(k5_numbers,B,k3_supinf_1,D,C)) = k1_funct_1(C,k5_setfam_1(A,k5_measure1(A,B,D))) ) ) ) ) ) )).

fof(t59_measure1,axiom,(
    $true )).

fof(t60_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => m1_measure1(C,A,B) ) ) )).

fof(t61_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_xboole_0(D,E)
                   => k1_measure1(B,C,k2_measure1(A,B,D,E)) = k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) )).

fof(t62_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_tarski(D,E)
                   => r1_supinf_1(k1_measure1(B,C,D),k1_measure1(B,C,E)) ) ) ) ) ) )).

fof(t63_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => ( r1_tarski(D,E)
                   => ( r1_supinf_1(k4_supinf_1,k1_measure1(B,C,D))
                      | k1_measure1(B,C,k4_measure1(A,B,E,D)) = k4_supinf_2(k1_measure1(B,C,E),k1_measure1(B,C,D)) ) ) ) ) ) ) )).

fof(t64_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m2_subset_1(E,k1_zfmisc_1(A),B)
                 => r1_supinf_1(k1_measure1(B,C,k2_measure1(A,B,D,E)),k2_supinf_2(k1_measure1(B,C,D),k1_measure1(B,C,E))) ) ) ) ) )).

fof(d12_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( r2_measure1(A,B,C,D)
            <=> r2_hidden(D,B) ) ) ) )).

fof(t65_measure1,axiom,(
    $true )).

fof(t66_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ( r2_measure1(A,B,C,k1_xboole_0)
            & r2_measure1(A,B,C,A)
            & ! [D,E] :
                ( ( r2_measure1(A,B,C,D)
                  & r2_measure1(A,B,C,E) )
               => ( r2_measure1(A,B,C,k4_xboole_0(A,D))
                  & r2_measure1(A,B,C,k2_xboole_0(D,E))
                  & r2_measure1(A,B,C,k3_xboole_0(D,E)) ) ) ) ) ) )).

fof(t67_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( ( ~ v1_xboole_0(D)
                & v1_card_4(D)
                & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
             => ( ! [E] :
                    ( r2_hidden(E,D)
                   => r2_measure1(A,B,C,E) )
               => ( r2_measure1(A,B,C,k5_setfam_1(A,D))
                  & r2_measure1(A,B,C,k6_setfam_1(A,D)) ) ) ) ) ) )).

fof(d13_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ( m4_measure1(D,A,B,C)
              <=> k1_measure1(B,C,D) = k1_supinf_2 ) ) ) ) )).

fof(t68_measure1,axiom,(
    $true )).

fof(t69_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m4_measure1(E,A,B,C)
                 => ( r1_tarski(D,E)
                   => m4_measure1(D,A,B,C) ) ) ) ) ) )).

fof(t70_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m4_measure1(D,A,B,C)
             => ! [E] :
                  ( m4_measure1(E,A,B,C)
                 => ( m4_measure1(k2_measure1(A,B,D,E),A,B,C)
                    & m4_measure1(k3_measure1(A,B,D,E),A,B,C)
                    & m4_measure1(k4_measure1(A,B,D,E),A,B,C) ) ) ) ) ) )).

fof(t71_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ! [D] :
              ( m2_subset_1(D,k1_zfmisc_1(A),B)
             => ! [E] :
                  ( m4_measure1(E,A,B,C)
                 => ( k1_measure1(B,C,k2_measure1(A,B,D,E)) = k1_measure1(B,C,D)
                    & k1_measure1(B,C,k3_measure1(A,B,D,E)) = k1_supinf_2
                    & k1_measure1(B,C,k4_measure1(A,B,D,E)) = k1_measure1(B,C,D) ) ) ) ) ) )).

fof(s1_measure1,axiom,
    ( ? [A] :
        ( r1_tarski(A,f1_s1_measure1)
        & p1_s1_measure1(A) )
   => ? [A] :
        ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(f1_s1_measure1)))
        & ! [B] :
            ( r2_hidden(B,A)
          <=> ( r1_tarski(B,f1_s1_measure1)
              & p1_s1_measure1(B) ) ) ) )).

fof(dt_m1_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m1_measure1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) ) ) ) )).

fof(existence_m1_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : m1_measure1(C,A,B) ) )).

fof(dt_m2_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure1(C,A,B) )
     => ! [D] :
          ( m2_measure1(D,A,B,C)
         => m2_subset_1(D,k1_zfmisc_1(A),B) ) ) )).

fof(existence_m2_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_measure1(C,A,B) )
     => ? [D] : m2_measure1(D,A,B,C) ) )).

fof(dt_m3_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ! [C] :
          ( m3_measure1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,B,k3_supinf_1)
            & m2_relset_1(C,B,k3_supinf_1) ) ) ) )).

fof(existence_m3_measure1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
     => ? [C] : m3_measure1(C,A,B) ) )).

fof(dt_m4_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m3_measure1(C,A,B) )
     => ! [D] :
          ( m4_measure1(D,A,B,C)
         => m2_subset_1(D,k1_zfmisc_1(A),B) ) ) )).

fof(existence_m4_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m3_measure1(C,A,B) )
     => ? [D] : m4_measure1(D,A,B,C) ) )).

fof(dt_k1_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_measure1(A,B,C),k3_supinf_1) ) )).

fof(redefinition_k1_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,k3_supinf_1)
        & m1_relset_1(B,A,k3_supinf_1)
        & m1_subset_1(C,A) )
     => k1_measure1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k2_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => m2_subset_1(k2_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) )).

fof(commutativity_k2_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,D) = k2_measure1(A,B,D,C) ) )).

fof(idempotence_k2_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,C) = C ) )).

fof(redefinition_k2_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v1_finsub_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k2_measure1(A,B,C,D) = k2_xboole_0(C,D) ) )).

fof(dt_k3_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => m2_subset_1(k3_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) )).

fof(commutativity_k3_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,D) = k3_measure1(A,B,D,C) ) )).

fof(idempotence_k3_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,C) = C ) )).

fof(redefinition_k3_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k3_measure1(A,B,C,D) = k3_xboole_0(C,D) ) )).

fof(dt_k4_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => m2_subset_1(k4_measure1(A,B,C,D),k1_zfmisc_1(A),B) ) )).

fof(redefinition_k4_measure1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(B)
        & v2_finsub_1(B)
        & v1_prob_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & m1_subset_1(C,B)
        & m1_subset_1(D,B) )
     => k4_measure1(A,B,C,D) = k4_xboole_0(C,D) ) )).

fof(dt_k5_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,B)
        & m1_relset_1(C,k5_numbers,B) )
     => ( ~ v1_xboole_0(k5_measure1(A,B,C))
        & m1_subset_1(k5_measure1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).

fof(redefinition_k5_measure1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_prob_1(B,A)
        & v1_measure1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
        & v1_funct_1(C)
        & v1_funct_2(C,k5_numbers,B)
        & m1_relset_1(C,k5_numbers,B) )
     => k5_measure1(A,B,C) = k2_relat_1(C) ) )).
%------------------------------------------------------------------------------