SET007 Axioms: SET007+20.ax
%------------------------------------------------------------------------------
% File : SET007+20 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Functions from a Set to a Set
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 214 ( 70 unt; 0 def)
% Number of atoms : 1129 ( 220 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 986 ( 71 ~; 28 |; 550 &)
% ( 14 <=>; 323 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 78 ( 78 usr; 39 con; 0-6 aty)
% Number of variables : 539 ( 515 !; 24 ?)
% 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_funct_2,axiom,
! [A,B] :
? [C] :
( m1_relset_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,A,B) ) ).
fof(cc1_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_partfun1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B) ) ) ) ).
fof(fc1_funct_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ~ v1_xboole_0(k1_funct_2(A,B)) ) ).
fof(fc2_funct_2,axiom,
! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ).
fof(cc2_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v3_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v2_funct_1(C)
& v1_funct_2(C,A,B)
& v2_funct_2(C,A,B) ) ) ) ).
fof(cc3_funct_2,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v2_funct_1(C)
& v1_funct_2(C,A,B)
& v2_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v3_funct_2(C,A,B) ) ) ) ).
fof(rc2_funct_2,axiom,
! [A] :
? [B] :
( m1_relset_1(B,A,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B)
& v1_funct_2(B,A,A)
& v2_funct_2(B,A,A)
& v3_funct_2(B,A,A) ) ).
fof(cc4_funct_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( ( v1_funct_1(B)
& v1_partfun1(B,A,A)
& v1_relat_2(B)
& v1_funct_2(B,A,A) )
=> ( v1_funct_1(B)
& v2_funct_1(B)
& v1_funct_2(B,A,A)
& v2_funct_2(B,A,A)
& v3_funct_2(B,A,A) ) ) ) ).
fof(cc5_funct_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_partfun1(C,A,B)
& v1_funct_2(C,A,B) ) ) ) ) ).
fof(cc6_funct_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_partfun1(C,A,B)
& v1_funct_2(C,A,B) ) ) ) ) ).
fof(d1_funct_2,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) ) )
& ( B = k1_xboole_0
=> ( A = k1_xboole_0
| ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 ) ) ) ) ) ).
fof(t1_funct_2,axiom,
$true ).
fof(t2_funct_2,axiom,
$true ).
fof(t3_funct_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_funct_1(A)
& v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
& m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ).
fof(t4_funct_2,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(k2_relat_1(B),A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k1_relat_1(B),A)
& m2_relset_1(B,k1_relat_1(B),A) ) ) ) ).
fof(t5_funct_2,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( k1_relat_1(C) = A
& ! [D] :
( r2_hidden(D,A)
=> r2_hidden(k1_funct_1(C,D),B) ) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) ) ) ) ).
fof(t6_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r2_hidden(C,A)
=> ( B = k1_xboole_0
| r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) ) ) ) ).
fof(t7_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r2_hidden(C,A)
=> ( B = k1_xboole_0
| r2_hidden(k1_funct_1(D,C),B) ) ) ) ).
fof(t8_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(k2_relat_1(D),C)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| ( v1_funct_1(D)
& v1_funct_2(D,A,C)
& m2_relset_1(D,A,C) ) ) ) ) ).
fof(t9_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(B,C)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| ( v1_funct_1(D)
& v1_funct_2(D,A,C)
& m2_relset_1(D,A,C) ) ) ) ) ).
fof(d2_funct_2,axiom,
! [A,B,C] :
( C = k1_funct_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_relat_1(E)
& v1_funct_1(E)
& D = E
& k1_relat_1(E) = A
& r1_tarski(k2_relat_1(E),B) ) ) ) ).
fof(t10_funct_2,axiom,
$true ).
fof(t11_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> r2_hidden(C,k1_funct_2(A,B)) ) ) ).
fof(t12_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> r2_hidden(B,k1_funct_2(A,A)) ) ).
fof(t13_funct_2,axiom,
$true ).
fof(t14_funct_2,axiom,
! [A] :
( A != k1_xboole_0
=> k1_funct_2(A,k1_xboole_0) = k1_xboole_0 ) ).
fof(t15_funct_2,axiom,
$true ).
fof(t16_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ! [D] :
~ ( r2_hidden(D,B)
& ! [E] :
~ ( r2_hidden(E,A)
& D = k1_funct_1(C,E) ) )
=> ( B = k1_xboole_0
| k2_relat_1(C) = B ) ) ) ).
fof(t17_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ~ ( r2_hidden(C,B)
& k2_relat_1(D) = B
& ! [E] :
~ ( r2_hidden(E,A)
& k1_funct_1(D,E) = C ) ) ) ).
fof(t18_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(C,E) = k1_funct_1(D,E) )
=> C = D ) ) ) ).
fof(t19_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( ~ ( B = k1_xboole_0
& C != k1_xboole_0
& A != k1_xboole_0 )
=> ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
& v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
& m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ).
fof(t20_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( ( k2_relat_1(D) = B
& k2_relat_1(E) = C )
=> ( B = k1_xboole_0
| C = k1_xboole_0
| k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C ) ) ) ) ).
fof(t21_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(C,A)
=> ( B = k1_xboole_0
| k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ).
fof(t22_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( B != k1_xboole_0
=> ( k2_relat_1(C) = B
<=> ! [D] :
( D != k1_xboole_0
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,D)
& m2_relset_1(E,B,D) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,D)
& m2_relset_1(F,B,D) )
=> ( k1_partfun1(A,B,B,D,C,E) = k1_partfun1(A,B,B,D,C,F)
=> E = F ) ) ) ) ) ) ) ).
fof(t23_funct_2,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
& k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ).
fof(t24_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ( k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B)
=> k2_relat_1(C) = B ) ) ) ).
fof(t25_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( v2_funct_1(C)
<=> ! [D,E] :
( ( r2_hidden(D,A)
& r2_hidden(E,A)
& k1_funct_1(C,D) = k1_funct_1(C,E) )
=> D = E ) ) ) ) ).
fof(t26_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( v2_funct_1(k1_partfun1(A,B,B,C,D,E))
=> ( ( C = k1_xboole_0
& B != k1_xboole_0 )
| ( B = k1_xboole_0
& A != k1_xboole_0 )
| v2_funct_1(D) ) ) ) ) ).
fof(t27_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ~ ( A != k1_xboole_0
& B != k1_xboole_0
& ~ ( v2_funct_1(C)
<=> ! [D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,D,A)
& m2_relset_1(E,D,A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,D,A)
& m2_relset_1(F,D,A) )
=> ( k1_partfun1(D,A,A,B,E,C) = k1_partfun1(D,A,A,B,F,C)
=> E = F ) ) ) ) ) ) ).
fof(t28_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( ( k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C
& v2_funct_1(E) )
=> ( C = k1_xboole_0
| k2_relat_1(D) = B ) ) ) ) ).
fof(t29_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ( k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)
=> ( B = k1_xboole_0
| ( v2_funct_1(C)
& k2_relat_1(D) = A ) ) ) ) ) ).
fof(t30_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ( ( v2_funct_1(k1_partfun1(A,B,B,C,D,E))
& k2_relat_1(D) = B )
=> ( ( C = k1_xboole_0
& B != k1_xboole_0 )
| ( v2_funct_1(D)
& v2_funct_1(E) ) ) ) ) ) ).
fof(t31_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( v2_funct_1(C)
& k2_relat_1(C) = B )
=> ( v1_funct_1(k2_funct_1(C))
& v1_funct_2(k2_funct_1(C),B,A)
& m2_relset_1(k2_funct_1(C),B,A) ) ) ) ).
fof(t32_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ( v2_funct_1(D)
& r2_hidden(C,A) )
=> ( B = k1_xboole_0
| k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C ) ) ) ).
fof(t33_funct_2,axiom,
$true ).
fof(t34_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ( ( k2_relat_1(C) = B
& v2_funct_1(C)
& ! [E,F] :
( ( ( r2_hidden(E,B)
& k1_funct_1(D,E) = F )
=> ( r2_hidden(F,A)
& k1_funct_1(C,F) = E ) )
& ( ( r2_hidden(F,A)
& k1_funct_1(C,F) = E )
=> ( r2_hidden(E,B)
& k1_funct_1(D,E) = F ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| D = k2_funct_1(C) ) ) ) ) ).
fof(t35_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( k2_relat_1(C) = B
& v2_funct_1(C) )
=> ( B = k1_xboole_0
| ( k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A)
& k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) ) ) ) ) ).
fof(t36_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ( ( k2_relat_1(C) = B
& k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)
& v2_funct_1(C) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| D = k2_funct_1(C) ) ) ) ) ).
fof(t37_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ~ ( B != k1_xboole_0
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A)
& k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) )
& ~ v2_funct_1(C) ) ) ).
fof(t38_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(C,A)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| ( v1_funct_1(k2_partfun1(A,B,D,C))
& v1_funct_2(k2_partfun1(A,B,D,C),C,B)
& m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) ).
fof(t39_funct_2,axiom,
$true ).
fof(t40_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(A,C)
=> k2_partfun1(A,B,D,C) = D ) ) ).
fof(t41_funct_2,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( ( r2_hidden(C,A)
& r2_hidden(k1_funct_1(E,C),D) )
=> ( B = k1_xboole_0
| k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) ) ) ) ).
fof(t42_funct_2,axiom,
$true ).
fof(t43_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( B != k1_xboole_0
=> ! [E] :
( ? [F] :
( r2_hidden(F,A)
& r2_hidden(F,C)
& E = k1_funct_1(D,F) )
=> r2_hidden(E,k9_relat_1(D,C)) ) ) ) ).
fof(t44_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> r1_tarski(k9_relat_1(D,C),B) ) ).
fof(t45_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> k2_funct_2(A,B,C,A) = k2_relat_1(C) ) ) ).
fof(t46_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( B != k1_xboole_0
=> ! [E] :
( r2_hidden(E,k10_relat_1(D,C))
<=> ( r2_hidden(E,A)
& r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ).
fof(t47_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> r1_tarski(k10_relat_1(D,C),A) ) ).
fof(t48_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> k3_funct_2(A,B,C,B) = A ) ) ).
fof(t49_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ! [D] :
~ ( r2_hidden(D,B)
& k3_funct_2(A,B,C,k1_tarski(D)) = k1_xboole_0 )
<=> k2_relat_1(C) = B ) ) ).
fof(t50_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(C,A)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) ) ) ) ).
fof(t51_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A ) ) ).
fof(t52_funct_2,axiom,
$true ).
fof(t53_funct_2,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,C)
& m2_relset_1(F,B,C) )
=> ~ ( ( C = k1_xboole_0
=> B = k1_xboole_0 )
& ( B = k1_xboole_0
=> A = k1_xboole_0 )
& ~ r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) ) ) ) ).
fof(t54_funct_2,axiom,
$true ).
fof(t55_funct_2,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k1_relat_1(B) = k1_xboole_0
=> ( v1_funct_1(B)
& v1_funct_2(B,k1_xboole_0,A)
& m2_relset_1(B,k1_xboole_0,A) ) ) ) ).
fof(t56_funct_2,axiom,
$true ).
fof(t57_funct_2,axiom,
$true ).
fof(t58_funct_2,axiom,
$true ).
fof(t59_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_xboole_0,A)
& m2_relset_1(C,k1_xboole_0,A) )
=> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0 ) ).
fof(t60_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_xboole_0,A)
& m2_relset_1(C,k1_xboole_0,A) )
=> k3_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0 ) ).
fof(t61_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_tarski(A),B)
& m2_relset_1(C,k1_tarski(A),B) )
=> ( B != k1_xboole_0
=> r2_hidden(k1_funct_1(C,A),B) ) ) ).
fof(t62_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_tarski(A),B)
& m2_relset_1(C,k1_tarski(A),B) )
=> ( B != k1_xboole_0
=> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A)) ) ) ).
fof(t63_funct_2,axiom,
$true ).
fof(t64_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_tarski(A),B)
& m2_relset_1(D,k1_tarski(A),B) )
=> ( B != k1_xboole_0
=> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A))) ) ) ).
fof(t65_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_tarski(B))
& m2_relset_1(D,A,k1_tarski(B)) )
=> ( r2_hidden(C,A)
=> k1_funct_1(D,C) = B ) ) ).
fof(t66_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_tarski(B))
& m2_relset_1(C,A,k1_tarski(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_tarski(B))
& m2_relset_1(D,A,k1_tarski(B)) )
=> C = D ) ) ).
fof(t67_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( k4_relset_1(A,A,B) = A
& r1_tarski(k2_relat_1(B),A) ) ) ).
fof(t68_funct_2,axiom,
$true ).
fof(t69_funct_2,axiom,
$true ).
fof(t70_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(B,A)
=> k1_funct_1(k5_relat_1(C,D),B) = k1_funct_1(D,k1_funct_1(C,B)) ) ) ) ).
fof(t71_funct_2,axiom,
$true ).
fof(t72_funct_2,axiom,
$true ).
fof(t73_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( ( k2_relat_1(B) = A
& k2_relat_1(C) = A )
=> k2_relat_1(k4_funct_2(A,B,C)) = A ) ) ) ).
fof(t74_funct_2,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ( k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B
& k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B ) ) ).
fof(t75_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( ( k4_funct_2(A,B,C) = B
& k2_relat_1(B) = A )
=> C = k6_partfun1(A) ) ) ) ).
fof(t76_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( ( k4_funct_2(A,C,B) = B
& v2_funct_1(B) )
=> C = k6_partfun1(A) ) ) ) ).
fof(t77_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( v2_funct_1(B)
<=> ! [C,D] :
( ( r2_hidden(C,A)
& r2_hidden(D,A)
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> C = D ) ) ) ).
fof(t78_funct_2,axiom,
$true ).
fof(t79_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k2_funct_2(A,A,B,A) = k2_relat_1(B) ) ).
fof(t80_funct_2,axiom,
$true ).
fof(t81_funct_2,axiom,
$true ).
fof(t82_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A ) ).
fof(d3_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_funct_2(C,A,B)
<=> k2_relat_1(C) = B ) ) ).
fof(d4_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v3_funct_2(C,A,B)
<=> ( v2_funct_1(C)
& v2_funct_2(C,A,B) ) ) ) ).
fof(t83_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( ( v2_funct_1(B)
& k2_relat_1(B) = A )
=> ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) ) ) ) ).
fof(t84_funct_2,axiom,
$true ).
fof(t85_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( v2_funct_1(B)
=> ! [C,D] :
( ( r2_hidden(C,A)
& r2_hidden(D,A)
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> C = D ) ) ) ).
fof(t86_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( k5_funct_2(A,B,C) = C
=> B = k6_partfun1(A) ) ) ) ).
fof(t87_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( k5_funct_2(A,B,C) = k6_partfun1(A)
=> C = k6_funct_2(A,B) ) ) ) ).
fof(t88_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ( k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A)
& k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A) ) ) ).
fof(t89_funct_2,axiom,
$true ).
fof(t90_funct_2,axiom,
$true ).
fof(t91_funct_2,axiom,
$true ).
fof(t92_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r1_tarski(B,A)
=> ( k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B
& k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B ) ) ) ).
fof(t93_funct_2,axiom,
$true ).
fof(t94_funct_2,axiom,
$true ).
fof(t95_funct_2,axiom,
$true ).
fof(t96_funct_2,axiom,
$true ).
fof(t97_funct_2,axiom,
$true ).
fof(t98_funct_2,axiom,
$true ).
fof(t99_funct_2,axiom,
$true ).
fof(t100_funct_2,axiom,
$true ).
fof(t101_funct_2,axiom,
$true ).
fof(t102_funct_2,axiom,
$true ).
fof(t103_funct_2,axiom,
$true ).
fof(t104_funct_2,axiom,
$true ).
fof(t105_funct_2,axiom,
$true ).
fof(t106_funct_2,axiom,
$true ).
fof(t107_funct_2,axiom,
$true ).
fof(t108_funct_2,axiom,
$true ).
fof(t109_funct_2,axiom,
$true ).
fof(t110_funct_2,axiom,
$true ).
fof(t111_funct_2,axiom,
$true ).
fof(t112_funct_2,axiom,
$true ).
fof(t113_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(C,E) = k1_funct_1(D,E) )
=> C = D ) ) ) ).
fof(t114_funct_2,axiom,
$true ).
fof(t115_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
& ! [F] :
~ ( r2_hidden(F,A)
& r2_hidden(F,C)
& E = k1_funct_1(D,F) ) ) ) ).
fof(t116_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
~ ( r2_hidden(E,k2_funct_2(A,B,D,C))
& ! [F] :
( m1_subset_1(F,A)
=> ~ ( r2_hidden(F,C)
& E = k1_funct_1(D,F) ) ) ) ) ).
fof(t117_funct_2,axiom,
$true ).
fof(t118_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m2_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,B),C)
& m2_relset_1(E,k2_zfmisc_1(A,B),C) )
=> ( ! [F,G] :
( ( r2_hidden(F,A)
& r2_hidden(G,B) )
=> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) )
=> D = E ) ) ) ).
fof(t119_funct_2,axiom,
! [A,B,C,D,E,F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,B),C)
& m2_relset_1(F,k2_zfmisc_1(A,B),C) )
=> ( ( r2_hidden(D,A)
& r2_hidden(E,B) )
=> ( C = k1_xboole_0
| r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) ) ) ) ).
fof(t120_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m2_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,B),C)
& m2_relset_1(E,k2_zfmisc_1(A,B),C) )
=> ( ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,B)
=> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)) ) )
=> D = E ) ) ) ).
fof(t121_funct_2,axiom,
! [A,B,C] :
( r2_hidden(C,k1_funct_2(A,B))
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) ) ) ).
fof(t122_funct_2,axiom,
$true ).
fof(t123_funct_2,axiom,
$true ).
fof(t124_funct_2,axiom,
$true ).
fof(t125_funct_2,axiom,
$true ).
fof(t126_funct_2,axiom,
$true ).
fof(t127_funct_2,axiom,
$true ).
fof(t128_funct_2,axiom,
$true ).
fof(t129_funct_2,axiom,
$true ).
fof(t130_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ( k4_relset_1(A,B,C) = A
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) ) ) ) ).
fof(t131_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ( v1_partfun1(C,A,B)
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) ) ) ) ).
fof(t132_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| v1_partfun1(C,A,B) ) ) ) ).
fof(t133_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> v1_partfun1(k3_partfun1(C,A,B),A,B) ) ) ).
fof(t134_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> v1_partfun1(k3_partfun1(B,A,A),A,A) ) ).
fof(t135_funct_2,axiom,
$true ).
fof(t136_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ~ ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ? [E] :
( r2_hidden(E,k4_relset_1(A,B,C))
& k1_funct_1(D,E) != k1_funct_1(C,E) ) ) ) ) ).
fof(t137_funct_2,axiom,
$true ).
fof(t138_funct_2,axiom,
$true ).
fof(t139_funct_2,axiom,
$true ).
fof(t140_funct_2,axiom,
$true ).
fof(t141_funct_2,axiom,
! [A,B] : r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B)) ).
fof(t142_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_partfun1(C,D)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| C = D ) ) ) ) ).
fof(t143_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r1_partfun1(B,C)
=> B = C ) ) ) ).
fof(t144_funct_2,axiom,
$true ).
fof(t145_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( r1_partfun1(C,D)
<=> ! [E] :
( r2_hidden(E,k4_relset_1(A,B,C))
=> k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) ) ) ).
fof(t146_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r1_partfun1(B,C)
<=> ! [D] :
( r2_hidden(D,k4_relset_1(A,A,B))
=> k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ).
fof(t147_funct_2,axiom,
$true ).
fof(t148_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ~ ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ~ r1_partfun1(C,D) ) ) ) ).
fof(t149_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,A) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A)
& r1_partfun1(B,C) ) ) ).
fof(t150_funct_2,axiom,
$true ).
fof(t151_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( ( r1_partfun1(C,E)
& r1_partfun1(D,E) )
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| r1_partfun1(C,D) ) ) ) ) ) ).
fof(t152_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( ( r1_partfun1(B,D)
& r1_partfun1(C,D) )
=> r1_partfun1(B,C) ) ) ) ) ).
fof(t153_funct_2,axiom,
$true ).
fof(t154_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ~ ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
& r1_partfun1(C,D)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ~ ( r1_partfun1(C,E)
& r1_partfun1(D,E) ) ) ) ) ) ).
fof(t155_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_partfun1(C,D)
=> ( ( B = k1_xboole_0
& A != k1_xboole_0 )
| r2_hidden(D,k5_partfun1(A,B,C)) ) ) ) ) ).
fof(t156_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r1_partfun1(B,C)
=> r2_hidden(C,k5_partfun1(A,A,B)) ) ) ) ).
fof(t157_funct_2,axiom,
$true ).
fof(t158_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( r2_hidden(D,k5_partfun1(A,B,C))
=> ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) ) ) ) ).
fof(t159_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)) ) ).
fof(t160_funct_2,axiom,
! [A,B] : k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B) ).
fof(t161_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C) ) ) ).
fof(t162_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B) ) ).
fof(t163_funct_2,axiom,
$true ).
fof(t164_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k1_tarski(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_tarski(B))
& m2_relset_1(D,A,k1_tarski(B)) )
=> k5_partfun1(A,k1_tarski(B),C) = k1_tarski(D) ) ) ).
fof(t165_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(D,C)
=> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) ) ) ).
fof(t166_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ( ( r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C))
& r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) )
=> r1_tarski(D,C) ) ) ) ).
fof(t167_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ( ( r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))
& ! [E] : B != k1_tarski(E) )
=> r1_tarski(D,C) ) ) ) ).
fof(t168_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,B) )
=> ( ( ! [E] : B != k1_tarski(E)
& k5_partfun1(A,B,C) = k5_partfun1(A,B,D) )
=> C = D ) ) ) ).
fof(d5_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
& m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) )
=> D = k9_funct_2(A,B,C) ) ).
fof(t169_funct_2,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_hidden(C,k1_funct_2(A,B))
=> ( k1_relat_1(C) = A
& r1_tarski(k2_relat_1(C),B) ) ) ) ).
fof(s1_funct_2,axiom,
( ! [A] :
~ ( r2_hidden(A,f1_s1_funct_2)
& ! [B] :
~ ( r2_hidden(B,f2_s1_funct_2)
& p1_s1_funct_2(A,B) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2)
& m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2)
& ! [B] :
( r2_hidden(B,f1_s1_funct_2)
=> p1_s1_funct_2(B,k1_funct_1(A,B)) ) ) ) ).
fof(s2_funct_2,axiom,
( ! [A] :
( r2_hidden(A,f1_s2_funct_2)
=> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2)
& m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2)
& ! [B] :
( r2_hidden(B,f1_s2_funct_2)
=> k1_funct_1(A,B) = f3_s2_funct_2(B) ) ) ) ).
fof(s3_funct_2,axiom,
( ! [A] :
( m1_subset_1(A,f1_s3_funct_2)
=> ? [B] :
( m1_subset_1(B,f2_s3_funct_2)
& p1_s3_funct_2(A,B) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2)
& m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s3_funct_2)
=> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)) ) ) ) ).
fof(s4_funct_2,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2)
& m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s4_funct_2)
=> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B) ) ) ).
fof(s5_funct_2,axiom,
( ! [A,B] :
~ ( r2_hidden(A,f1_s5_funct_2)
& r2_hidden(B,f2_s5_funct_2)
& ! [C] :
~ ( r2_hidden(C,f3_s5_funct_2)
& p1_s5_funct_2(A,B,C) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2)
& m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2)
& ! [B,C] :
( ( r2_hidden(B,f1_s5_funct_2)
& r2_hidden(C,f2_s5_funct_2) )
=> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))) ) ) ) ).
fof(s6_funct_2,axiom,
( ! [A,B] :
( ( r2_hidden(A,f1_s6_funct_2)
& r2_hidden(B,f2_s6_funct_2) )
=> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2)
& m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2)
& ! [B,C] :
( ( r2_hidden(B,f1_s6_funct_2)
& r2_hidden(C,f2_s6_funct_2) )
=> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C) ) ) ) ).
fof(s7_funct_2,axiom,
( ! [A] :
( m1_subset_1(A,f1_s7_funct_2)
=> ! [B] :
( m1_subset_1(B,f2_s7_funct_2)
=> ? [C] :
( m1_subset_1(C,f3_s7_funct_2)
& p1_s7_funct_2(A,B,C) ) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2)
& m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s7_funct_2)
=> ! [C] :
( m1_subset_1(C,f2_s7_funct_2)
=> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))) ) ) ) ) ).
fof(s8_funct_2,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2)
& m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s8_funct_2)
=> ! [C] :
( m1_subset_1(C,f2_s8_funct_2)
=> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C) ) ) ) ).
fof(s9_funct_2,axiom,
( ! [A] :
( r2_hidden(A,f1_s9_funct_2)
=> ( ( p1_s9_funct_2(A)
=> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2) )
& ( ~ p1_s9_funct_2(A)
=> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2) ) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2)
& m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2)
& ! [B] :
( r2_hidden(B,f1_s9_funct_2)
=> ( ( p1_s9_funct_2(B)
=> k1_funct_1(A,B) = f3_s9_funct_2(B) )
& ( ~ p1_s9_funct_2(B)
=> k1_funct_1(A,B) = f4_s9_funct_2(B) ) ) ) ) ) ).
fof(s10_funct_2,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2)
& m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2)
& k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2
& ! [B] :
( m1_subset_1(B,f1_s10_funct_2)
=> ( B != f3_s10_funct_2
=> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B) ) ) ) ).
fof(s11_funct_2,axiom,
( f3_s11_funct_2 != f4_s11_funct_2
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2)
& m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2)
& k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2
& k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2
& ! [B] :
( m1_subset_1(B,f1_s11_funct_2)
=> ~ ( B != f3_s11_funct_2
& B != f4_s11_funct_2
& k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) ) ) ) ) ).
fof(s12_funct_2,axiom,
( ! [A] :
( m1_subset_1(A,f1_s12_funct_2)
=> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2)
& m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s12_funct_2)
=> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B) ) ) ) ).
fof(s13_funct_2,axiom,
( ! [A] :
( m1_subset_1(A,f1_s13_funct_2)
=> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2)
& m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s13_funct_2)
=> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B) ) ) ) ).
fof(s14_funct_2,axiom,
( ! [A] :
( m1_subset_1(A,f1_s14_funct_2)
=> ? [B] :
( m1_subset_1(B,f2_s14_funct_2)
& p1_s14_funct_2(A,B) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2)
& m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2)
& ! [B] :
( m1_subset_1(B,f1_s14_funct_2)
=> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)) ) ) ) ).
fof(dt_k1_funct_2,axiom,
$true ).
fof(dt_k2_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ).
fof(redefinition_k2_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ).
fof(dt_k3_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)) ) ).
fof(redefinition_k3_funct_2,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& m1_relset_1(C,A,B) )
=> k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ) ).
fof(dt_k4_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v1_funct_1(k4_funct_2(A,B,C))
& v1_funct_2(k4_funct_2(A,B,C),A,A)
& m2_relset_1(k4_funct_2(A,B,C),A,A) ) ) ).
fof(redefinition_k4_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> k4_funct_2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k5_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v1_funct_1(k5_funct_2(A,B,C))
& v1_funct_2(k5_funct_2(A,B,C),A,A)
& v3_funct_2(k5_funct_2(A,B,C),A,A)
& m2_relset_1(k5_funct_2(A,B,C),A,A) ) ) ).
fof(redefinition_k5_funct_2,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> k5_funct_2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k6_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> ( v1_funct_1(k6_funct_2(A,B))
& v1_funct_2(k6_funct_2(A,B),A,A)
& v3_funct_2(k6_funct_2(A,B),A,A)
& m2_relset_1(k6_funct_2(A,B),A,A) ) ) ).
fof(redefinition_k6_funct_2,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> k6_funct_2(A,B) = k2_funct_1(B) ) ).
fof(dt_k7_funct_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B)
& v1_funct_1(E)
& v1_funct_2(E,B,C)
& m1_relset_1(E,B,C) )
=> ( v1_funct_1(k7_funct_2(A,B,C,D,E))
& v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
& m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k7_funct_2,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B)
& v1_funct_1(E)
& v1_funct_2(E,B,C)
& m1_relset_1(E,B,C) )
=> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ).
fof(dt_k8_funct_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> m1_subset_1(k8_funct_2(A,B,C,D),B) ) ).
fof(redefinition_k8_funct_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k9_funct_2,axiom,
! [A,B,C] :
( v1_funct_1(k9_funct_2(A,B,C))
& v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
& m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) ) ).
%------------------------------------------------------------------------------