SET007 Axioms: SET007+161.ax
%------------------------------------------------------------------------------
% File : SET007+161 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 745 ( 90 equ)
% Maximal formula atoms : 17 ( 8 avg)
% Number of connectives : 961 ( 307 ~; 7 |; 344 &)
% ( 16 <=>; 287 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 279 ( 263 !; 16 ?)
% 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 ).
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