SET007 Axioms: SET007+161.ax


%------------------------------------------------------------------------------
% File     : SET007+161 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Properties of the Intervals of Real Numbers
% 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    : measure5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   91 (   9 unit)
%            Number of atoms       :  745 (  90 equality)
%            Maximal formula depth :   20 (  12 average)
%            Number of connectives :  961 ( 307 ~  ;   7  |; 344  &)
%                                         (  16 <=>; 287 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   18 (   1 propositional; 0-2 arity)
%            Number of functors    :   19 (   7 constant; 0-2 arity)
%            Number of variables   :  279 (   0 singleton; 263 !;  16 ?)
%            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(rc1_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_membered(A)
      & v2_membered(A)
      & v1_measure5(A) ) )).

fof(rc2_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_membered(A)
      & v2_membered(A)
      & v2_measure5(A) ) )).

fof(rc3_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_membered(A)
      & v2_membered(A)
      & v3_measure5(A) ) )).

fof(rc4_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_membered(A)
      & v2_membered(A)
      & v4_measure5(A) ) )).

fof(rc5_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_membered(A)
      & v2_membered(A)
      & v5_measure5(A) ) )).

fof(cc1_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v1_measure5(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v5_measure5(A) ) ) ) )).

fof(cc2_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v2_measure5(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v5_measure5(A) ) ) ) )).

fof(cc3_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v3_measure5(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v5_measure5(A) ) ) ) )).

fof(cc4_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v4_measure5(A)
       => ( v1_membered(A)
          & v2_membered(A)
          & v5_measure5(A) ) ) ) )).

fof(rc6_measure5,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
      & v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A)
      & v5_measure5(A) ) )).

fof(t1_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(A,B)
           => ( A = k5_supinf_1
              | A = k4_supinf_1
              | r1_supinf_1(k1_supinf_2,k4_supinf_2(B,A)) ) ) ) ) )).

fof(t2_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(A,B)
           => ( ( A = k5_supinf_1
                & B = k5_supinf_1 )
              | ( A = k4_supinf_1
                & B = k4_supinf_1 )
              | r1_supinf_1(k1_supinf_2,k4_supinf_2(B,A)) ) ) ) ) )).

fof(t3_measure5,axiom,(
    $true )).

fof(t4_measure5,axiom,(
    $true )).

fof(t5_measure5,axiom,(
    $true )).

fof(t6_measure5,axiom,(
    $true )).

fof(t7_measure5,axiom,(
    $true )).

fof(t8_measure5,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)
             => ~ ( B != k5_supinf_1
                  & B != k4_supinf_1
                  & ~ ( A = k5_supinf_1
                      & C = k5_supinf_1 )
                  & ~ ( A = k4_supinf_1
                      & C = k4_supinf_1 )
                  & k2_supinf_2(k4_supinf_2(C,B),k4_supinf_2(B,A)) != k4_supinf_2(C,A) ) ) ) ) )).

fof(t9_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(k10_supinf_1(k12_supinf_1(A,B)),A)
            & r1_supinf_1(k10_supinf_1(k12_supinf_1(A,B)),B)
            & r1_supinf_1(A,k9_supinf_1(k12_supinf_1(A,B)))
            & r1_supinf_1(B,k9_supinf_1(k12_supinf_1(A,B))) ) ) ) )).

fof(d1_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k6_supinf_1))
             => ( C = k1_measure5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( r2_hidden(D,C)
                    <=> ( r1_supinf_1(A,D)
                        & r1_supinf_1(D,B)
                        & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) ) )).

fof(d2_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k6_supinf_1))
             => ( C = k2_measure5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( r2_hidden(D,C)
                    <=> ( ~ r1_supinf_1(D,A)
                        & ~ r1_supinf_1(B,D)
                        & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) ) )).

fof(d3_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k6_supinf_1))
             => ( C = k3_measure5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( r2_hidden(D,C)
                    <=> ( ~ r1_supinf_1(D,A)
                        & r1_supinf_1(D,B)
                        & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) ) )).

fof(d4_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(k6_supinf_1))
             => ( C = k4_measure5(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                   => ( r2_hidden(D,C)
                    <=> ( r1_supinf_1(A,D)
                        & ~ r1_supinf_1(B,D)
                        & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) ) )).

fof(d5_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v1_measure5(A)
      <=> ? [B] :
            ( m1_subset_1(B,k3_supinf_1)
            & ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r1_supinf_1(B,C)
                & A = k2_measure5(B,C) ) ) ) ) )).

fof(d6_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v2_measure5(A)
      <=> ? [B] :
            ( m1_subset_1(B,k3_supinf_1)
            & ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r1_supinf_1(B,C)
                & A = k1_measure5(B,C) ) ) ) ) )).

fof(d7_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v3_measure5(A)
      <=> ? [B] :
            ( m1_subset_1(B,k3_supinf_1)
            & ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r1_supinf_1(B,C)
                & A = k4_measure5(B,C) ) ) ) ) )).

fof(d8_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v4_measure5(A)
      <=> ? [B] :
            ( m1_subset_1(B,k3_supinf_1)
            & ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & r1_supinf_1(B,C)
                & A = k3_measure5(B,C) ) ) ) ) )).

fof(d9_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ( v5_measure5(A)
      <=> ~ ( ~ v1_measure5(A)
            & ~ v2_measure5(A)
            & ~ v3_measure5(A)
            & ~ v4_measure5(A) ) ) ) )).

fof(t10_measure5,axiom,(
    $true )).

fof(t11_measure5,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k3_supinf_1)
     => ! [C] :
          ( m1_subset_1(C,k3_supinf_1)
         => ( ~ ( ~ r2_hidden(A,k2_measure5(B,C))
                & ~ r2_hidden(A,k1_measure5(B,C))
                & ~ r2_hidden(A,k4_measure5(B,C))
                & ~ r2_hidden(A,k3_measure5(B,C)) )
           => m1_subset_1(A,k3_supinf_1) ) ) ) )).

fof(t12_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( ~ r1_supinf_1(A,B)
           => ( k2_measure5(A,B) = k1_xboole_0
              & k1_measure5(A,B) = k1_xboole_0
              & k4_measure5(A,B) = k1_xboole_0
              & k3_measure5(A,B) = k1_xboole_0 ) ) ) ) )).

fof(t13_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( k2_measure5(A,A) = k1_xboole_0
        & k4_measure5(A,A) = k1_xboole_0
        & k3_measure5(A,A) = k1_xboole_0 ) ) )).

fof(t14_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ( ( ( A = k5_supinf_1
            | A = k4_supinf_1 )
         => k1_measure5(A,A) = k1_xboole_0 )
        & ~ ( A != k5_supinf_1
            & A != k4_supinf_1
            & k1_measure5(A,A) != k11_supinf_1(A) ) ) ) )).

fof(t15_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(B,A)
           => ( k2_measure5(A,B) = k1_xboole_0
              & k4_measure5(A,B) = k1_xboole_0
              & k3_measure5(A,B) = k1_xboole_0
              & r1_tarski(k1_measure5(A,B),k11_supinf_1(A))
              & r1_tarski(k1_measure5(A,B),k11_supinf_1(B)) ) ) ) ) )).

fof(t16_measure5,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)
                  & ~ r2_hidden(B,k6_supinf_1) ) ) ) ) )).

fof(t17_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ r1_supinf_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ~ ( ~ r1_supinf_1(C,A)
                      & ~ r1_supinf_1(B,C)
                      & r2_hidden(C,k6_supinf_1) ) ) ) ) ) )).

fof(t18_measure5,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,A)
                  & ! [D] :
                      ( m1_subset_1(D,k3_supinf_1)
                     => ~ ( ~ r1_supinf_1(D,A)
                          & ~ r1_supinf_1(B,D)
                          & ~ r1_supinf_1(C,D)
                          & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) )).

fof(t19_measure5,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(C,A)
                  & ~ r1_supinf_1(C,B)
                  & ! [D] :
                      ( m1_subset_1(D,k3_supinf_1)
                     => ~ ( ~ r1_supinf_1(D,A)
                          & ~ r1_supinf_1(D,B)
                          & ~ r1_supinf_1(C,D)
                          & r2_hidden(D,k6_supinf_1) ) ) ) ) ) ) )).

fof(t20_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(A,C))
                                & ~ r2_hidden(E,k2_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(A,C))
                                & r2_hidden(E,k2_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t21_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(C,A))
                                & ~ r2_hidden(E,k2_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(C,A))
                                & r2_hidden(E,k2_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t22_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(A,C))
                                & ~ r2_hidden(E,k2_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(A,C))
                                & r2_hidden(E,k2_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t23_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(C,A))
                                & ~ r2_hidden(E,k2_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(C,A))
                                & r2_hidden(E,k2_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t24_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(A,C))
                                & ~ r2_hidden(E,k1_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(A,C))
                                & r2_hidden(E,k1_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t25_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(C,A))
                                & ~ r2_hidden(E,k1_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(C,A))
                                & r2_hidden(E,k1_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t26_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(A,C))
                                & ~ r2_hidden(E,k4_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(A,C))
                                & r2_hidden(E,k4_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t27_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(C,A))
                                & ~ r2_hidden(E,k4_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(C,A))
                                & r2_hidden(E,k4_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t28_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(A,C))
                                & ~ r2_hidden(E,k2_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(A,C))
                                & r2_hidden(E,k2_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t29_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(C,A))
                                & ~ r2_hidden(E,k2_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(C,A))
                                & r2_hidden(E,k2_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t30_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(A,C))
                                & ~ r2_hidden(E,k3_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(A,C))
                                & r2_hidden(E,k3_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t31_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k2_measure5(C,A))
                                & ~ r2_hidden(E,k3_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k2_measure5(C,A))
                                & r2_hidden(E,k3_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t32_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(A,C))
                                & ~ r2_hidden(E,k2_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(A,C))
                                & r2_hidden(E,k2_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t33_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(C,A))
                                & ~ r2_hidden(E,k2_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(C,A))
                                & r2_hidden(E,k2_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t34_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(A,C))
                                & ~ r2_hidden(E,k1_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(A,C))
                                & r2_hidden(E,k1_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t35_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(C,A))
                                & ~ r2_hidden(E,k1_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(C,A))
                                & r2_hidden(E,k1_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t36_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(A,C))
                                & ~ r2_hidden(E,k4_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(A,C))
                                & r2_hidden(E,k4_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t37_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(C,A))
                                & ~ r2_hidden(E,k4_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(C,A))
                                & r2_hidden(E,k4_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t38_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(A,C))
                                & ~ r2_hidden(E,k1_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(A,C))
                                & r2_hidden(E,k1_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t39_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(C,A))
                                & ~ r2_hidden(E,k1_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(C,A))
                                & r2_hidden(E,k1_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t40_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(A,C))
                                & ~ r2_hidden(E,k3_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(A,C))
                                & r2_hidden(E,k3_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t41_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k1_measure5(C,A))
                                & ~ r2_hidden(E,k3_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k1_measure5(C,A))
                                & r2_hidden(E,k3_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t42_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(A,C))
                                & ~ r2_hidden(E,k1_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(A,C))
                                & r2_hidden(E,k1_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t43_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(C,A))
                                & ~ r2_hidden(E,k1_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(C,A))
                                & r2_hidden(E,k1_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t44_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(A,C))
                                & ~ r2_hidden(E,k4_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(A,C))
                                & r2_hidden(E,k4_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t45_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(C,A))
                                & ~ r2_hidden(E,k4_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(C,A))
                                & r2_hidden(E,k4_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t46_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(A,C))
                                & ~ r2_hidden(E,k3_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(A,C))
                                & r2_hidden(E,k3_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t47_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k4_measure5(C,A))
                                & ~ r2_hidden(E,k3_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k4_measure5(C,A))
                                & r2_hidden(E,k3_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t48_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(A,C))
                                & ~ r2_hidden(E,k4_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(A,C))
                                & r2_hidden(E,k4_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t49_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(C,A))
                                & ~ r2_hidden(E,k4_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(C,A))
                                & r2_hidden(E,k4_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t50_measure5,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(B,A)
                      & ~ ( r1_supinf_1(C,A)
                          & r1_supinf_1(D,B) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(A,C))
                                & ~ r2_hidden(E,k3_measure5(B,D)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(A,C))
                                & r2_hidden(E,k3_measure5(B,D)) ) ) ) ) ) ) ) ) )).

fof(t51_measure5,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(B,A)
                      & ~ ( r1_supinf_1(A,C)
                          & r1_supinf_1(B,D) )
                      & ! [E] :
                          ( m1_subset_1(E,k3_supinf_1)
                         => ( ~ ( r2_hidden(E,k3_measure5(C,A))
                                & ~ r2_hidden(E,k3_measure5(D,B)) )
                            & ~ ( ~ r2_hidden(E,k3_measure5(C,A))
                                & r2_hidden(E,k3_measure5(D,B)) ) ) ) ) ) ) ) ) )).

fof(t52_measure5,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)
                 => ! [E] :
                      ( ( v5_measure5(E)
                        & m1_subset_1(E,k1_zfmisc_1(k6_supinf_1)) )
                     => ~ ( ~ r1_supinf_1(B,A)
                          & ~ ( E != k2_measure5(A,B)
                              & E != k1_measure5(A,B)
                              & E != k4_measure5(A,B)
                              & E != k3_measure5(A,B) )
                          & ~ ( E != k2_measure5(C,D)
                              & E != k1_measure5(C,D)
                              & E != k4_measure5(C,D)
                              & E != k3_measure5(C,D) )
                          & ~ ( A = C
                              & B = D ) ) ) ) ) ) ) )).

fof(d10_measure5,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ( B = k5_measure5(A)
          <=> ? [C] :
                ( m1_subset_1(C,k3_supinf_1)
                & ? [D] :
                    ( m1_subset_1(D,k3_supinf_1)
                    & ~ ( A != k2_measure5(C,D)
                        & A != k1_measure5(C,D)
                        & A != k4_measure5(C,D)
                        & A != k3_measure5(C,D) )
                    & ( ~ r1_supinf_1(D,C)
                     => B = k4_supinf_2(D,C) )
                    & ( r1_supinf_1(D,C)
                     => B = k1_supinf_2 ) ) ) ) ) ) )).

fof(t53_measure5,axiom,(
    ! [A] :
      ( ( v1_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)
             => ( A = k2_measure5(B,C)
               => ( ( ~ r1_supinf_1(C,B)
                   => k5_measure5(A) = k4_supinf_2(C,B) )
                  & ( r1_supinf_1(C,B)
                   => k5_measure5(A) = k1_supinf_2 ) ) ) ) ) ) )).

fof(t54_measure5,axiom,(
    ! [A] :
      ( ( v2_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)
             => ( A = k1_measure5(B,C)
               => ( ( ~ r1_supinf_1(C,B)
                   => k5_measure5(A) = k4_supinf_2(C,B) )
                  & ( r1_supinf_1(C,B)
                   => k5_measure5(A) = k1_supinf_2 ) ) ) ) ) ) )).

fof(t55_measure5,axiom,(
    ! [A] :
      ( ( v3_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)
             => ( A = k4_measure5(B,C)
               => ( ( ~ r1_supinf_1(C,B)
                   => k5_measure5(A) = k4_supinf_2(C,B) )
                  & ( r1_supinf_1(C,B)
                   => k5_measure5(A) = k1_supinf_2 ) ) ) ) ) ) )).

fof(t56_measure5,axiom,(
    ! [A] :
      ( ( v4_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)
             => ( A = k3_measure5(B,C)
               => ( ( ~ r1_supinf_1(C,B)
                   => k5_measure5(A) = k4_supinf_2(C,B) )
                  & ( r1_supinf_1(C,B)
                   => k5_measure5(A) = k1_supinf_2 ) ) ) ) ) ) )).

fof(t57_measure5,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,k3_supinf_1)
                 => ( ( B = k5_supinf_1
                      & r2_hidden(C,k6_supinf_1)
                      & D = k4_supinf_1 )
                   => ( ( A != k2_measure5(B,C)
                        & A != k2_measure5(C,D)
                        & A != k1_measure5(B,C)
                        & A != k1_measure5(C,D)
                        & A != k4_measure5(B,C)
                        & A != k4_measure5(C,D)
                        & A != k3_measure5(B,C)
                        & A != k3_measure5(C,D) )
                      | k5_measure5(A) = k4_supinf_1 ) ) ) ) ) ) )).

fof(t58_measure5,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)
             => ( ( B = k5_supinf_1
                  & C = k4_supinf_1 )
               => ( ( A != k2_measure5(B,C)
                    & A != k1_measure5(B,C)
                    & A != k4_measure5(B,C)
                    & A != k3_measure5(B,C) )
                  | k5_measure5(A) = k4_supinf_1 ) ) ) ) ) )).

fof(t59_measure5,axiom,(
    $true )).

fof(t60_measure5,axiom,(
    k5_measure5(k6_measure5) = k1_supinf_2 )).

fof(t61_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] :
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] :
              ( ( v5_measure5(C)
                & m1_subset_1(C,k1_zfmisc_1(k6_supinf_1)) )
             => ! [D] :
                  ( ( v5_measure5(D)
                    & m1_subset_1(D,k1_zfmisc_1(k6_supinf_1)) )
                 => ( ( r1_tarski(C,D)
                      & D = k1_measure5(A,B)
                      & r1_supinf_1(B,A) )
                   => ( k5_measure5(C) = k1_supinf_2
                      & k5_measure5(D) = k1_supinf_2 ) ) ) ) ) ) )).

fof(t62_measure5,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_tarski(A,B)
           => r1_supinf_1(k5_measure5(A),k5_measure5(B)) ) ) ) )).

fof(t63_measure5,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => r1_supinf_1(k1_supinf_2,k5_measure5(A)) ) )).

fof(s1_measure5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k6_supinf_1))
         => ( ( ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( r2_hidden(C,A)
                  <=> p1_s1_measure5(C) ) )
              & ! [C] :
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( r2_hidden(C,B)
                  <=> p1_s1_measure5(C) ) ) )
           => A = B ) ) ) )).

fof(dt_k1_measure5,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k1_measure5(A,B),k1_zfmisc_1(k6_supinf_1)) ) )).

fof(dt_k2_measure5,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_measure5(A,B),k1_zfmisc_1(k6_supinf_1)) ) )).

fof(dt_k3_measure5,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k3_measure5(A,B),k1_zfmisc_1(k6_supinf_1)) ) )).

fof(dt_k4_measure5,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k4_measure5(A,B),k1_zfmisc_1(k6_supinf_1)) ) )).

fof(dt_k5_measure5,axiom,(
    ! [A] :
      ( ( v5_measure5(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => m1_subset_1(k5_measure5(A),k3_supinf_1) ) )).

fof(dt_k6_measure5,axiom,
    ( v1_xboole_0(k6_measure5)
    & v5_measure5(k6_measure5)
    & m1_subset_1(k6_measure5,k1_zfmisc_1(k6_supinf_1)) )).

fof(redefinition_k6_measure5,axiom,(
    k6_measure5 = k1_xboole_0 )).
%------------------------------------------------------------------------------