SET007 Axioms: SET007+328.ax


%------------------------------------------------------------------------------
% File     : SET007+328 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  304 (  95 equality)
%            Maximal formula depth :   26 (   5 average)
%            Number of connectives :  241 (   9 ~  ;   0  |; 180  &)
%                                         (   0 <=>;  52 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    9 (   1 propositional; 0-2 arity)
%            Number of functors    :   35 (   2 constant; 0-3 arity)
%            Number of variables   :   66 (   0 singleton;  66 !;   0 ?)
%            Maximal term depth    :    6 (   3 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(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)) ) )).
%------------------------------------------------------------------------------