SET007 Axioms: SET007+61.ax
%------------------------------------------------------------------------------
% File : SET007+61 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Curried and Uncurried Functions
% 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 : funct_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 86 ( 12 unt; 0 def)
% Number of atoms : 403 ( 126 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 332 ( 15 ~; 10 |; 183 &)
% ( 8 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 2 con; 0-2 aty)
% Number of variables : 213 ( 207 !; 6 ?)
% 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(t1_funct_5,axiom,
k2_funct_4(k1_xboole_0) = k1_xboole_0 ).
fof(d1_funct_5,axiom,
! [A,B] :
( B = k1_funct_5(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ).
fof(d2_funct_5,axiom,
! [A,B] :
( B = k2_funct_5(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ).
fof(t2_funct_5,axiom,
$true ).
fof(t3_funct_5,axiom,
$true ).
fof(t4_funct_5,axiom,
! [A,B,C] :
( r2_hidden(k4_tarski(A,B),C)
=> ( r2_hidden(A,k1_funct_5(C))
& r2_hidden(B,k2_funct_5(C)) ) ) ).
fof(t5_funct_5,axiom,
! [A,B] :
( r1_tarski(A,B)
=> ( r1_tarski(k1_funct_5(A),k1_funct_5(B))
& r1_tarski(k2_funct_5(A),k2_funct_5(B)) ) ) ).
fof(t6_funct_5,axiom,
! [A,B] :
( k1_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k1_funct_5(A),k1_funct_5(B))
& k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) ) ).
fof(t7_funct_5,axiom,
! [A,B] :
( r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B)))
& r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) ) ).
fof(t8_funct_5,axiom,
! [A,B] :
( r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B)))
& r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) ) ).
fof(t9_funct_5,axiom,
! [A,B] :
( r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B)))
& r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))) ) ).
fof(t10_funct_5,axiom,
( k1_funct_5(k1_xboole_0) = k1_xboole_0
& k2_funct_5(k1_xboole_0) = k1_xboole_0 ) ).
fof(t11_funct_5,axiom,
! [A,B] :
( ~ ( A = k1_xboole_0
& k2_zfmisc_1(B,A) = k1_xboole_0
& k2_zfmisc_1(A,B) = k1_xboole_0 )
=> ( k1_funct_5(k2_zfmisc_1(B,A)) = B
& k2_funct_5(k2_zfmisc_1(A,B)) = B ) ) ).
fof(t12_funct_5,axiom,
! [A,B] :
( r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A)
& r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) ) ).
fof(t13_funct_5,axiom,
! [A,B,C] :
( r1_tarski(A,k2_zfmisc_1(B,C))
=> ( r1_tarski(k1_funct_5(A),B)
& r1_tarski(k2_funct_5(A),C) ) ) ).
fof(t14_funct_5,axiom,
$true ).
fof(t15_funct_5,axiom,
! [A,B] :
( k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A)
& k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B) ) ).
fof(t16_funct_5,axiom,
! [A,B,C,D] :
( k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C)
& k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D) ) ).
fof(t17_funct_5,axiom,
! [A] :
( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A)
=> ( k1_funct_5(A) = k1_xboole_0
& k2_funct_5(A) = k1_xboole_0 ) ) ).
fof(t18_funct_5,axiom,
! [A] :
( ( k1_funct_5(A) = k1_xboole_0
| k2_funct_5(A) = k1_xboole_0 )
=> ! [B,C] : ~ r2_hidden(k4_tarski(B,C),A) ) ).
fof(t19_funct_5,axiom,
! [A] :
( k1_funct_5(A) = k1_xboole_0
<=> k2_funct_5(A) = k1_xboole_0 ) ).
fof(t20_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A)))
& k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))) ) ) ).
fof(t21_funct_5,axiom,
! [A] :
( v1_relat_1(A)
=> ( k1_funct_5(A) = k1_relat_1(A)
& k2_funct_5(A) = k2_relat_1(A) ) ) ).
fof(d3_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( B = k3_funct_5(A)
<=> ( k1_relat_1(B) = k1_funct_5(k1_relat_1(A))
& ! [C] :
~ ( r2_hidden(C,k1_funct_5(k1_relat_1(A)))
& ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ~ ( k1_funct_1(B,C) = D
& k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A)))))
& ! [E] :
( r2_hidden(E,k1_relat_1(D))
=> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)) ) ) ) ) ) ) ) ) ).
fof(d4_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( B = k4_funct_5(A)
<=> ( ! [C] :
( r2_hidden(C,k1_relat_1(B))
<=> ? [D,E] :
( v1_relat_1(E)
& v1_funct_1(E)
& ? [F] :
( C = k4_tarski(D,F)
& r2_hidden(D,k1_relat_1(A))
& E = k1_funct_1(A,D)
& r2_hidden(F,k1_relat_1(E)) ) ) )
& ! [C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(C,k1_relat_1(B))
& D = k1_funct_1(A,k1_mcart_1(C)) )
=> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)) ) ) ) ) ) ) ).
fof(d5_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k5_funct_5(A) = k3_funct_5(k2_funct_4(A)) ) ).
fof(d6_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)) ) ).
fof(t22_funct_5,axiom,
$true ).
fof(t23_funct_5,axiom,
$true ).
fof(t24_funct_5,axiom,
$true ).
fof(t25_funct_5,axiom,
$true ).
fof(t26_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
=> ( r2_hidden(A,k1_relat_1(k3_funct_5(C)))
& v1_relat_1(k1_funct_1(k3_funct_5(C),A))
& v1_funct_1(k1_funct_1(k3_funct_5(C),A)) ) ) ) ).
fof(t27_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
& D = k1_funct_1(k3_funct_5(C),A) )
=> ( r2_hidden(B,k1_relat_1(D))
& k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B)) ) ) ) ) ).
fof(t28_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
=> ( r2_hidden(B,k1_relat_1(k5_funct_5(C)))
& v1_relat_1(k1_funct_1(k5_funct_5(C),B))
& v1_funct_1(k1_funct_1(k5_funct_5(C),B)) ) ) ) ).
fof(t29_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
& D = k1_funct_1(k5_funct_5(C),B) )
=> ( r2_hidden(A,k1_relat_1(D))
& k1_funct_1(D,A) = k1_funct_1(C,k4_tarski(A,B)) ) ) ) ) ).
fof(t30_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k1_relat_1(k5_funct_5(A)) = k2_funct_5(k1_relat_1(A)) ) ).
fof(t31_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( k1_relat_1(C) = k2_zfmisc_1(A,B)
=> ( k2_zfmisc_1(A,B) = k1_xboole_0
| ( k1_relat_1(k3_funct_5(C)) = A
& k1_relat_1(k5_funct_5(C)) = B ) ) ) ) ).
fof(t32_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
=> ( r1_tarski(k1_relat_1(k3_funct_5(C)),A)
& r1_tarski(k1_relat_1(k5_funct_5(C)),B) ) ) ) ).
fof(t33_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
=> ( k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A)
& k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C)) ) ) ) ).
fof(t34_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ! [B,C] : ~ r2_hidden(k4_tarski(B,C),k1_relat_1(A))
=> ( k3_funct_5(A) = k1_xboole_0
& k5_funct_5(A) = k1_xboole_0 ) ) ) ).
fof(t35_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ! [B] :
~ ( r2_hidden(B,k1_relat_1(A))
& v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B)) )
=> ( k4_funct_5(A) = k1_xboole_0
& k6_funct_5(A) = k1_xboole_0 ) ) ) ).
fof(t36_funct_5,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
& k1_relat_1(D) = k2_zfmisc_1(A,B)
& r2_hidden(C,A)
& ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ~ ( k1_funct_1(k3_funct_5(D),C) = E
& k1_relat_1(E) = B
& r1_tarski(k2_relat_1(E),k2_relat_1(D))
& ! [F] :
( r2_hidden(F,B)
=> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F)) ) ) ) ) ) ).
fof(t37_funct_5,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(A,k1_relat_1(k3_funct_5(B)))
=> ( v1_relat_1(k1_funct_1(k3_funct_5(B),A))
& v1_funct_1(k1_funct_1(k3_funct_5(B),A)) ) ) ) ).
fof(t38_funct_5,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k1_relat_1(k3_funct_5(B)))
& C = k1_funct_1(k3_funct_5(B),A) )
=> ( k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B)))))
& r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B)))
& r1_tarski(k2_relat_1(C),k2_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> ( k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(A,D))
& r2_hidden(k4_tarski(A,D),k1_relat_1(B)) ) ) ) ) ) ) ).
fof(t39_funct_5,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ~ ( k2_zfmisc_1(A,B) != k1_xboole_0
& k1_relat_1(D) = k2_zfmisc_1(A,B)
& r2_hidden(C,B)
& ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ~ ( k1_funct_1(k5_funct_5(D),C) = E
& k1_relat_1(E) = A
& r1_tarski(k2_relat_1(E),k2_relat_1(D))
& ! [F] :
( r2_hidden(F,A)
=> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)) ) ) ) ) ) ).
fof(t40_funct_5,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(A,k1_relat_1(k5_funct_5(B)))
=> ( v1_relat_1(k1_funct_1(k5_funct_5(B),A))
& v1_funct_1(k1_funct_1(k5_funct_5(B),A)) ) ) ) ).
fof(t41_funct_5,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(A,k1_relat_1(k5_funct_5(B)))
& C = k1_funct_1(k5_funct_5(B),A) )
=> ( k1_relat_1(C) = k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A))))
& r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B)))
& r1_tarski(k2_relat_1(C),k2_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> ( k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(D,A))
& r2_hidden(k4_tarski(D,A),k1_relat_1(B)) ) ) ) ) ) ) ).
fof(t42_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( k1_relat_1(C) = k2_zfmisc_1(A,B)
=> ( r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))
& r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) ) ) ) ).
fof(t43_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A)))
& r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))) ) ) ).
fof(t44_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
=> ( r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))
& r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) ) ) ) ).
fof(t45_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(A,k1_relat_1(C))
& D = k1_funct_1(C,A)
& r2_hidden(B,k1_relat_1(D)) )
=> ( r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C)))
& k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)
& r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) ) ) ) ) ).
fof(t46_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r2_hidden(A,k1_relat_1(C))
& D = k1_funct_1(C,A)
& r2_hidden(B,k1_relat_1(D)) )
=> ( r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))
& k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) = k1_funct_1(D,B)
& r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) ) ) ) ) ).
fof(t47_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
=> ( r1_tarski(k2_relat_1(k4_funct_5(C)),B)
& r1_tarski(k2_relat_1(k6_funct_5(C)),B) ) ) ) ).
fof(t48_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
=> ( r1_tarski(k2_relat_1(k4_funct_5(C)),B)
& r1_tarski(k2_relat_1(k6_funct_5(C)),B) ) ) ) ).
fof(t49_funct_5,axiom,
( k3_funct_5(k1_xboole_0) = k1_xboole_0
& k5_funct_5(k1_xboole_0) = k1_xboole_0 ) ).
fof(t50_funct_5,axiom,
( k4_funct_5(k1_xboole_0) = k1_xboole_0
& k6_funct_5(k1_xboole_0) = k1_xboole_0 ) ).
fof(t51_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( k1_relat_1(C) = k2_zfmisc_1(A,B)
& k1_relat_1(D) = k2_zfmisc_1(A,B)
& k3_funct_5(C) = k3_funct_5(D) )
=> C = D ) ) ) ).
fof(t52_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( k1_relat_1(C) = k2_zfmisc_1(A,B)
& k1_relat_1(D) = k2_zfmisc_1(A,B)
& k5_funct_5(C) = k5_funct_5(D) )
=> C = D ) ) ) ).
fof(t53_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
& r1_tarski(k2_relat_1(D),k1_funct_2(A,B))
& k4_funct_5(C) = k4_funct_5(D) )
=> ( A = k1_xboole_0
| C = D ) ) ) ) ).
fof(t54_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
& r1_tarski(k2_relat_1(D),k1_funct_2(A,B))
& k6_funct_5(C) = k6_funct_5(D) )
=> ( A = k1_xboole_0
| C = D ) ) ) ) ).
fof(t55_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
=> ( A = k1_xboole_0
| ( k3_funct_5(k4_funct_5(C)) = C
& k5_funct_5(k6_funct_5(C)) = C ) ) ) ) ).
fof(t56_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( k1_relat_1(C) = k2_zfmisc_1(A,B)
=> ( k4_funct_5(k3_funct_5(C)) = C
& k6_funct_5(k5_funct_5(C)) = C ) ) ) ).
fof(t57_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
=> ( k4_funct_5(k3_funct_5(C)) = C
& k6_funct_5(k5_funct_5(C)) = C ) ) ) ).
fof(t58_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
=> ( r2_hidden(k1_xboole_0,k2_relat_1(C))
| ( k3_funct_5(k4_funct_5(C)) = C
& k5_funct_5(k6_funct_5(C)) = C ) ) ) ) ).
fof(t59_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
& r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B))
& k3_funct_5(C) = k3_funct_5(D) )
=> C = D ) ) ) ).
fof(t60_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B))
& r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B))
& k5_funct_5(C) = k5_funct_5(D) )
=> C = D ) ) ) ).
fof(t61_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
& r1_tarski(k2_relat_1(D),k4_partfun1(A,B))
& k4_funct_5(C) = k4_funct_5(D) )
=> ( r2_hidden(k1_xboole_0,k2_relat_1(C))
| r2_hidden(k1_xboole_0,k2_relat_1(D))
| C = D ) ) ) ) ).
fof(t62_funct_5,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_tarski(k2_relat_1(C),k4_partfun1(A,B))
& r1_tarski(k2_relat_1(D),k4_partfun1(A,B))
& k6_funct_5(C) = k6_funct_5(D) )
=> ( r2_hidden(k1_xboole_0,k2_relat_1(C))
| r2_hidden(k1_xboole_0,k2_relat_1(D))
| C = D ) ) ) ) ).
fof(t63_funct_5,axiom,
! [A,B,C] :
( r1_tarski(A,B)
=> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)) ) ).
fof(t64_funct_5,axiom,
! [A] : k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0) ).
fof(t65_funct_5,axiom,
! [A,B] :
( r2_wellord2(A,k1_funct_2(k1_tarski(B),A))
& k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)) ) ).
fof(t66_funct_5,axiom,
! [A,B] : k1_funct_2(A,k1_tarski(B)) = k1_tarski(k2_funcop_1(A,B)) ).
fof(t67_funct_5,axiom,
! [A,B,C,D] :
( ( r2_wellord2(A,B)
& r2_wellord2(C,D) )
=> ( r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D))
& k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) ) ).
fof(t68_funct_5,axiom,
! [A,B,C,D] :
( ( k1_card_1(A) = k1_card_1(B)
& k1_card_1(C) = k1_card_1(D) )
=> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) ) ).
fof(t69_funct_5,axiom,
! [A,B,C] :
( r1_xboole_0(A,B)
=> ( r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C)))
& k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) ) ) ).
fof(t70_funct_5,axiom,
! [A,B,C] :
( r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C)))
& k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) ) ).
fof(t71_funct_5,axiom,
! [A,B,C] :
( r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C)))
& k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) ) ).
fof(t72_funct_5,axiom,
! [A,B,C] :
( A != B
=> ( r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C))
& k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)) ) ) ).
fof(t73_funct_5,axiom,
! [A,B,C] :
( A != B
=> ( r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C))
& k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,C)) ) ) ).
fof(s1_funct_5,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& k1_relat_1(A) = f1_s1_funct_5
& ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,f1_s1_funct_5)
=> k1_funct_1(A,B) = f2_s1_funct_5(B) ) ) ) ).
fof(dt_k1_funct_5,axiom,
$true ).
fof(dt_k2_funct_5,axiom,
$true ).
fof(dt_k3_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k3_funct_5(A))
& v1_funct_1(k3_funct_5(A)) ) ) ).
fof(dt_k4_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k4_funct_5(A))
& v1_funct_1(k4_funct_5(A)) ) ) ).
fof(dt_k5_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k5_funct_5(A))
& v1_funct_1(k5_funct_5(A)) ) ) ).
fof(dt_k6_funct_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k6_funct_5(A))
& v1_funct_1(k6_funct_5(A)) ) ) ).
%------------------------------------------------------------------------------