SET007 Axioms: SET007+328.ax
%------------------------------------------------------------------------------
% File : SET007+328 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Definitions of Petri Net. Part I
% 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 : ff_siec [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 72 ( 13 unt; 0 def)
% Number of atoms : 304 ( 95 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 241 ( 9 ~; 0 |; 180 &)
% ( 0 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 2 con; 0-3 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% 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(d1_ff_siec,axiom,
$true ).
fof(d2_ff_siec,axiom,
! [A] :
( l1_net_1(A)
=> k1_ff_siec(A) = k2_xboole_0(k1_net_1(A),k1_tarski(k1_net_1(A))) ) ).
fof(d3_ff_siec,axiom,
$true ).
fof(d4_ff_siec,axiom,
! [A,B] :
( r1_xboole_0(A,B)
=> k2_ff_siec(A,B) = g1_net_1(A,B,k1_xboole_0) ) ).
fof(d5_ff_siec,axiom,
! [A] : k3_ff_siec(A) = k2_ff_siec(A,k1_xboole_0) ).
fof(d6_ff_siec,axiom,
! [A] : k4_ff_siec(A) = k2_ff_siec(k1_xboole_0,A) ).
fof(d7_ff_siec,axiom,
! [A] : k5_ff_siec(A) = k2_ff_siec(k1_xboole_0,k1_tarski(A)) ).
fof(d8_ff_siec,axiom,
! [A] : k6_ff_siec(A) = k2_ff_siec(k1_tarski(A),k1_xboole_0) ).
fof(d9_ff_siec,axiom,
k7_ff_siec = k2_ff_siec(k1_xboole_0,k1_xboole_0) ).
fof(t1_ff_siec,axiom,
$true ).
fof(t2_ff_siec,axiom,
! [A,B] :
( r1_xboole_0(A,B)
=> ( u1_net_1(k2_ff_siec(A,B)) = A
& u2_net_1(k2_ff_siec(A,B)) = B
& u3_net_1(k2_ff_siec(A,B)) = k1_xboole_0 ) ) ).
fof(t3_ff_siec,axiom,
! [A] :
( u1_net_1(k3_ff_siec(A)) = A
& u2_net_1(k3_ff_siec(A)) = k1_xboole_0
& u3_net_1(k3_ff_siec(A)) = k1_xboole_0 ) ).
fof(t4_ff_siec,axiom,
! [A] :
( u1_net_1(k4_ff_siec(A)) = k1_xboole_0
& u2_net_1(k4_ff_siec(A)) = A
& u3_net_1(k4_ff_siec(A)) = k1_xboole_0 ) ).
fof(t5_ff_siec,axiom,
! [A] :
( u1_net_1(k5_ff_siec(A)) = k1_xboole_0
& u2_net_1(k5_ff_siec(A)) = k1_tarski(A)
& u3_net_1(k5_ff_siec(A)) = k1_xboole_0 ) ).
fof(t6_ff_siec,axiom,
! [A] :
( u1_net_1(k6_ff_siec(A)) = k1_tarski(A)
& u2_net_1(k6_ff_siec(A)) = k1_xboole_0
& u3_net_1(k6_ff_siec(A)) = k1_xboole_0 ) ).
fof(t7_ff_siec,axiom,
( u1_net_1(k7_ff_siec) = k1_xboole_0
& u2_net_1(k7_ff_siec) = k1_xboole_0
& u3_net_1(k7_ff_siec) = k1_xboole_0 ) ).
fof(t8_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(u1_net_1(A),k1_net_1(A))
& r1_tarski(u2_net_1(A),k1_net_1(A)) ) ) ).
fof(t9_ff_siec,axiom,
$true ).
fof(t10_ff_siec,axiom,
$true ).
fof(t11_ff_siec,axiom,
! [A,B,C] :
( ( v2_net_1(C)
& l1_net_1(C) )
=> ( ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
& r2_hidden(A,u2_net_1(C)) )
=> ( ~ r2_hidden(A,u1_net_1(C))
& ~ r2_hidden(B,u2_net_1(C))
& r2_hidden(B,u1_net_1(C)) ) )
& ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
& r2_hidden(B,u2_net_1(C)) )
=> ( ~ r2_hidden(B,u1_net_1(C))
& ~ r2_hidden(A,u2_net_1(C))
& r2_hidden(A,u1_net_1(C)) ) )
& ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
& r2_hidden(A,u1_net_1(C)) )
=> ( ~ r2_hidden(B,u1_net_1(C))
& ~ r2_hidden(A,u2_net_1(C))
& r2_hidden(B,u2_net_1(C)) ) )
& ( ( r2_hidden(k4_tarski(A,B),u3_net_1(C))
& r2_hidden(B,u1_net_1(C)) )
=> ( ~ r2_hidden(A,u1_net_1(C))
& ~ r2_hidden(B,u2_net_1(C))
& r2_hidden(A,u2_net_1(C)) ) ) ) ) ).
fof(t12_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k1_ff_siec(A) != k1_xboole_0 ) ).
fof(t13_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(u3_net_1(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
& r1_tarski(k4_relat_1(u3_net_1(A)),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ).
fof(t14_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),u1_net_1(A))
& r1_tarski(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),u1_net_1(A))
& r1_tarski(k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),u2_net_1(A))
& r1_tarski(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),u2_net_1(A))
& r1_tarski(k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),u2_net_1(A))
& r1_tarski(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),u2_net_1(A))
& r1_tarski(k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),u1_net_1(A))
& r1_tarski(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),u1_net_1(A))
& r1_tarski(k2_relat_1(k6_relat_1(u2_net_1(A))),u2_net_1(A))
& r1_tarski(k1_relat_1(k6_relat_1(u2_net_1(A))),u2_net_1(A))
& r1_tarski(k2_relat_1(k6_relat_1(u1_net_1(A))),u1_net_1(A))
& r1_tarski(k1_relat_1(k6_relat_1(u1_net_1(A))),u1_net_1(A)) ) ) ).
fof(t15_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k1_relat_1(k6_relat_1(u2_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k1_relat_1(k6_relat_1(u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k2_relat_1(k6_relat_1(u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k2_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k2_relat_1(k6_relat_1(u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k1_relat_1(k6_relat_1(u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))))
& r1_xboole_0(k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k1_relat_1(k6_relat_1(u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k2_relat_1(k6_relat_1(u2_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k2_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k2_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))))
& r1_xboole_0(k1_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k2_relat_1(k6_relat_1(u2_net_1(A)))) ) ) ).
fof(t16_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A)),k7_relat_1(u3_net_1(A),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k7_relat_1(u3_net_1(A),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)),k7_relat_1(u3_net_1(A),u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k7_relat_1(u3_net_1(A),u1_net_1(A))) = k1_xboole_0 ) ) ).
fof(t17_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u1_net_1(A))) = k7_relat_1(u3_net_1(A),u2_net_1(A))
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))
& k5_relat_1(k6_relat_1(u2_net_1(A)),k7_relat_1(u3_net_1(A),u2_net_1(A))) = k7_relat_1(u3_net_1(A),u2_net_1(A))
& k5_relat_1(k6_relat_1(u2_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))
& k5_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u2_net_1(A))) = k7_relat_1(u3_net_1(A),u1_net_1(A))
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u2_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))
& k5_relat_1(k6_relat_1(u1_net_1(A)),k7_relat_1(u3_net_1(A),u1_net_1(A))) = k7_relat_1(u3_net_1(A),u1_net_1(A))
& k5_relat_1(k6_relat_1(u1_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))
& k5_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u2_net_1(A))) = k7_relat_1(u3_net_1(A),u1_net_1(A))
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u2_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))
& k5_relat_1(k6_relat_1(u2_net_1(A)),k7_relat_1(u3_net_1(A),u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k6_relat_1(u2_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u1_net_1(A))) = k1_xboole_0
& k5_relat_1(k6_relat_1(u1_net_1(A)),k7_relat_1(u3_net_1(A),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k6_relat_1(u1_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u2_net_1(A))) = k1_xboole_0
& k5_relat_1(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u2_net_1(A))) = k1_xboole_0 ) ) ).
fof(t18_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(k1_net_1(A)))
& r1_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(k1_net_1(A)))
& r1_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(k1_net_1(A)))
& r1_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(k1_net_1(A))) ) ) ).
fof(t19_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k4_xboole_0(k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u1_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u1_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(u3_net_1(A),u2_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u1_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u1_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(u3_net_1(A),u1_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u2_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u2_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(u3_net_1(A),u1_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u2_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))
& k4_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u2_net_1(A))),k6_relat_1(k1_net_1(A))) = k7_relat_1(u3_net_1(A),u2_net_1(A)) ) ) ).
fof(t20_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k4_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))
& k4_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))) = k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)) ) ) ).
fof(t21_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k2_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k7_relat_1(u3_net_1(A),u2_net_1(A))) = u3_net_1(A)
& k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k7_relat_1(u3_net_1(A),u1_net_1(A))) = u3_net_1(A)
& k2_xboole_0(k4_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A))),k4_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A)))) = k4_relat_1(u3_net_1(A))
& k2_xboole_0(k4_relat_1(k7_relat_1(u3_net_1(A),u2_net_1(A))),k4_relat_1(k7_relat_1(u3_net_1(A),u1_net_1(A)))) = k4_relat_1(u3_net_1(A)) ) ) ).
fof(d10_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k8_ff_siec(A) = k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)),k6_relat_1(u1_net_1(A))) ) ).
fof(d11_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k9_ff_siec(A) = k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k6_relat_1(u1_net_1(A))) ) ).
fof(t22_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k9_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
& r1_tarski(k8_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ).
fof(t23_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k1_relat_1(k9_ff_siec(A)),k1_net_1(A))
& r1_tarski(k2_relat_1(k9_ff_siec(A)),k1_net_1(A))
& r1_tarski(k1_relat_1(k8_ff_siec(A)),k1_net_1(A))
& r1_tarski(k2_relat_1(k8_ff_siec(A)),k1_net_1(A)) ) ) ).
fof(t24_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k9_ff_siec(A),k9_ff_siec(A)) = k9_ff_siec(A)
& k5_relat_1(k9_ff_siec(A),k8_ff_siec(A)) = k9_ff_siec(A)
& k5_relat_1(k8_ff_siec(A),k8_ff_siec(A)) = k8_ff_siec(A)
& k5_relat_1(k8_ff_siec(A),k9_ff_siec(A)) = k8_ff_siec(A) ) ) ).
fof(t25_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k9_ff_siec(A),k4_xboole_0(k9_ff_siec(A),k6_relat_1(k1_net_1(A)))) = k1_xboole_0
& k5_relat_1(k8_ff_siec(A),k4_xboole_0(k8_ff_siec(A),k6_relat_1(k1_net_1(A)))) = k1_xboole_0 ) ) ).
fof(d12_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k10_ff_siec(A) = k2_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A))),k6_relat_1(u1_net_1(A))) ) ).
fof(d13_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k11_ff_siec(A) = k2_xboole_0(u3_net_1(A),k6_relat_1(k1_net_1(A))) ) ).
fof(t26_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k10_ff_siec(A),k10_ff_siec(A)) = k10_ff_siec(A)
& k5_relat_1(k4_xboole_0(k10_ff_siec(A),k6_relat_1(k1_net_1(A))),k10_ff_siec(A)) = k1_xboole_0
& k2_xboole_0(k2_xboole_0(k10_ff_siec(A),k4_relat_1(k10_ff_siec(A))),k6_relat_1(k1_net_1(A))) = k2_xboole_0(k11_ff_siec(A),k4_relat_1(k11_ff_siec(A))) ) ) ).
fof(d14_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k12_ff_siec(A) = u1_net_1(A) ) ).
fof(d15_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k13_ff_siec(A) = u2_net_1(A) ) ).
fof(d16_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k14_ff_siec(A) = k7_relat_1(u3_net_1(A),u2_net_1(A)) ) ).
fof(d17_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k15_ff_siec(A) = k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A)) ) ).
fof(t27_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k14_ff_siec(A),k2_zfmisc_1(k13_ff_siec(A),k12_ff_siec(A)))
& r1_tarski(k15_ff_siec(A),k2_zfmisc_1(k13_ff_siec(A),k12_ff_siec(A))) ) ) ).
fof(t28_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> r1_xboole_0(k12_ff_siec(A),k13_ff_siec(A)) ) ).
fof(t29_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k10_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
& r1_tarski(k11_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ).
fof(d18_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k16_ff_siec(A) = k2_xboole_0(k7_relat_1(k4_relat_1(u3_net_1(A)),u1_net_1(A)),k6_relat_1(u2_net_1(A))) ) ).
fof(d19_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k17_ff_siec(A) = k2_xboole_0(k7_relat_1(u3_net_1(A),u1_net_1(A)),k6_relat_1(u2_net_1(A))) ) ).
fof(t30_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k17_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A)))
& r1_tarski(k16_ff_siec(A),k2_zfmisc_1(k1_net_1(A),k1_net_1(A))) ) ) ).
fof(t31_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( r1_tarski(k1_relat_1(k17_ff_siec(A)),k1_net_1(A))
& r1_tarski(k2_relat_1(k17_ff_siec(A)),k1_net_1(A))
& r1_tarski(k1_relat_1(k16_ff_siec(A)),k1_net_1(A))
& r1_tarski(k2_relat_1(k16_ff_siec(A)),k1_net_1(A)) ) ) ).
fof(t32_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k17_ff_siec(A),k17_ff_siec(A)) = k17_ff_siec(A)
& k5_relat_1(k17_ff_siec(A),k16_ff_siec(A)) = k17_ff_siec(A)
& k5_relat_1(k16_ff_siec(A),k16_ff_siec(A)) = k16_ff_siec(A)
& k5_relat_1(k16_ff_siec(A),k17_ff_siec(A)) = k16_ff_siec(A) ) ) ).
fof(t33_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k17_ff_siec(A),k4_xboole_0(k17_ff_siec(A),k6_relat_1(k1_net_1(A)))) = k1_xboole_0
& k5_relat_1(k16_ff_siec(A),k4_xboole_0(k16_ff_siec(A),k6_relat_1(k1_net_1(A)))) = k1_xboole_0 ) ) ).
fof(d20_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> k18_ff_siec(A) = k2_xboole_0(k2_xboole_0(k7_relat_1(u3_net_1(A),u2_net_1(A)),k7_relat_1(k4_relat_1(u3_net_1(A)),u2_net_1(A))),k6_relat_1(u2_net_1(A))) ) ).
fof(t34_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> ( k5_relat_1(k18_ff_siec(A),k18_ff_siec(A)) = k18_ff_siec(A)
& k5_relat_1(k4_xboole_0(k18_ff_siec(A),k6_relat_1(k1_net_1(A))),k18_ff_siec(A)) = k1_xboole_0
& k2_xboole_0(k2_xboole_0(k18_ff_siec(A),k4_relat_1(k18_ff_siec(A))),k6_relat_1(k1_net_1(A))) = k2_xboole_0(k11_ff_siec(A),k4_relat_1(k11_ff_siec(A))) ) ) ).
fof(dt_k1_ff_siec,axiom,
$true ).
fof(dt_k2_ff_siec,axiom,
! [A,B] :
( v1_net_1(k2_ff_siec(A,B))
& v2_net_1(k2_ff_siec(A,B))
& l1_net_1(k2_ff_siec(A,B)) ) ).
fof(dt_k3_ff_siec,axiom,
! [A] :
( v1_net_1(k3_ff_siec(A))
& v2_net_1(k3_ff_siec(A))
& l1_net_1(k3_ff_siec(A)) ) ).
fof(dt_k4_ff_siec,axiom,
! [A] :
( v1_net_1(k4_ff_siec(A))
& v2_net_1(k4_ff_siec(A))
& l1_net_1(k4_ff_siec(A)) ) ).
fof(dt_k5_ff_siec,axiom,
! [A] :
( v1_net_1(k5_ff_siec(A))
& v2_net_1(k5_ff_siec(A))
& l1_net_1(k5_ff_siec(A)) ) ).
fof(dt_k6_ff_siec,axiom,
! [A] :
( v1_net_1(k6_ff_siec(A))
& v2_net_1(k6_ff_siec(A))
& l1_net_1(k6_ff_siec(A)) ) ).
fof(dt_k7_ff_siec,axiom,
( v1_net_1(k7_ff_siec)
& v2_net_1(k7_ff_siec)
& l1_net_1(k7_ff_siec) ) ).
fof(dt_k8_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k8_ff_siec(A)) ) ).
fof(dt_k9_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k9_ff_siec(A)) ) ).
fof(dt_k10_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k10_ff_siec(A)) ) ).
fof(dt_k11_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k11_ff_siec(A)) ) ).
fof(dt_k12_ff_siec,axiom,
$true ).
fof(dt_k13_ff_siec,axiom,
$true ).
fof(dt_k14_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k14_ff_siec(A)) ) ).
fof(dt_k15_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k15_ff_siec(A)) ) ).
fof(dt_k16_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k16_ff_siec(A)) ) ).
fof(dt_k17_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k17_ff_siec(A)) ) ).
fof(dt_k18_ff_siec,axiom,
! [A] :
( ( v2_net_1(A)
& l1_net_1(A) )
=> v1_relat_1(k18_ff_siec(A)) ) ).
%------------------------------------------------------------------------------