SET007 Axioms: SET007+329.ax


%------------------------------------------------------------------------------
% File     : SET007+329 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Definitions of Petri Net. Part II
% 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    : e_siec [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   99 (  21 unit)
%            Number of atoms       :  356 (  93 equality)
%            Maximal formula depth :   14 (   4 average)
%            Number of connectives :  261 (   4 ~  ;   1  |; 191  &)
%                                         (   3 <=>;  62 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   11 (   1 propositional; 0-2 arity)
%            Number of functors    :   36 (   2 constant; 0-3 arity)
%            Number of variables   :   97 (   0 singleton;  92 !;   5 ?)
%            Maximal term depth    :    7 (   2 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(rc1_e_siec,axiom,(
    ? [A] :
      ( l1_e_siec(A)
      & v1_e_siec(A) ) )).

fof(rc2_e_siec,axiom,(
    ? [A] :
      ( l1_e_siec(A)
      & v2_e_siec(A) ) )).

fof(rc3_e_siec,axiom,(
    ? [A] :
      ( l1_e_siec(A)
      & v3_e_siec(A) ) )).

fof(rc4_e_siec,axiom,(
    ? [A] :
      ( l1_e_siec(A)
      & v1_e_siec(A)
      & v2_e_siec(A)
      & v3_e_siec(A) ) )).

fof(d1_e_siec,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => k1_e_siec(A) = k2_xboole_0(u1_struct_0(A),k1_tarski(u1_struct_0(A))) ) )).

fof(d2_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => ( v2_e_siec(A)
      <=> ( r1_tarski(u1_e_siec(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
          & r1_tarski(u2_e_siec(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
          & k5_relat_1(u1_e_siec(A),u1_e_siec(A)) = u1_e_siec(A)
          & k5_relat_1(u1_e_siec(A),u2_e_siec(A)) = u1_e_siec(A)
          & k5_relat_1(u2_e_siec(A),u2_e_siec(A)) = u2_e_siec(A)
          & k5_relat_1(u2_e_siec(A),u1_e_siec(A)) = u2_e_siec(A) ) ) ) )).

fof(d3_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => ( v3_e_siec(A)
      <=> ( k5_relat_1(u1_e_siec(A),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
          & k5_relat_1(u2_e_siec(A),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) ) )).

fof(t1_e_siec,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( ( v2_e_siec(g1_e_siec(A,B,C))
              & v3_e_siec(g1_e_siec(A,B,C))
              & l1_e_siec(g1_e_siec(A,B,C)) )
          <=> ( r1_tarski(B,k2_zfmisc_1(A,A))
              & r1_tarski(C,k2_zfmisc_1(A,A))
              & k5_relat_1(B,B) = B
              & k5_relat_1(B,C) = B
              & k5_relat_1(C,C) = C
              & k5_relat_1(C,B) = C
              & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0
              & k5_relat_1(C,k4_xboole_0(C,k6_relat_1(A))) = k1_xboole_0 ) ) ) ) )).

fof(t2_e_siec,axiom,(
    ! [A] :
      ( v2_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0))
      & v3_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0))
      & l1_e_siec(g1_e_siec(A,k1_xboole_0,k1_xboole_0)) ) )).

fof(t3_e_siec,axiom,(
    ! [A] :
      ( v2_e_siec(g1_e_siec(A,k6_relat_1(A),k6_relat_1(A)))
      & v3_e_siec(g1_e_siec(A,k6_relat_1(A),k6_relat_1(A)))
      & l1_e_siec(g1_e_siec(A,k6_relat_1(A),k6_relat_1(A))) ) )).

fof(t4_e_siec,axiom,
    ( v2_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0))
    & v3_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0))
    & l1_e_siec(g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0)) )).

fof(t5_e_siec,axiom,(
    $true )).

fof(t6_e_siec,axiom,(
    $true )).

fof(t7_e_siec,axiom,(
    $true )).

fof(t8_e_siec,axiom,(
    ! [A,B] :
      ( v2_e_siec(g1_e_siec(A,k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(k4_xboole_0(A,B))))
      & v3_e_siec(g1_e_siec(A,k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(k4_xboole_0(A,B))))
      & l1_e_siec(g1_e_siec(A,k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(k4_xboole_0(A,B)))) ) )).

fof(t9_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k1_e_siec(A) != k1_xboole_0 ) )).

fof(d4_e_siec,axiom,(
    k2_e_siec = g1_e_siec(k1_xboole_0,k1_xboole_0,k1_xboole_0) )).

fof(d5_e_siec,axiom,(
    ! [A] : k3_e_siec(A) = g1_e_siec(A,k6_relat_1(A),k6_relat_1(A)) )).

fof(d6_e_siec,axiom,(
    ! [A] : k4_e_siec(A) = g1_e_siec(A,k1_xboole_0,k1_xboole_0) )).

fof(t10_e_siec,axiom,(
    $true )).

fof(t11_e_siec,axiom,(
    ! [A] :
      ( u1_struct_0(k3_e_siec(A)) = A
      & u1_e_siec(k3_e_siec(A)) = k6_relat_1(A)
      & u2_e_siec(k3_e_siec(A)) = k6_relat_1(A) ) )).

fof(t12_e_siec,axiom,(
    ! [A] :
      ( u1_struct_0(k4_e_siec(A)) = A
      & u1_e_siec(k4_e_siec(A)) = k1_xboole_0
      & u2_e_siec(k4_e_siec(A)) = k1_xboole_0 ) )).

fof(d7_e_siec,axiom,(
    ! [A] : k5_e_siec(A) = g1_e_siec(k1_tarski(A),k6_relat_1(k1_tarski(A)),k6_relat_1(k1_tarski(A))) )).

fof(d8_e_siec,axiom,(
    ! [A] : k6_e_siec(A) = g1_e_siec(k1_tarski(A),k1_xboole_0,k1_xboole_0) )).

fof(t13_e_siec,axiom,(
    ! [A] :
      ( u1_struct_0(k5_e_siec(A)) = k1_tarski(A)
      & u1_e_siec(k5_e_siec(A)) = k6_relat_1(k1_tarski(A))
      & u2_e_siec(k5_e_siec(A)) = k6_relat_1(k1_tarski(A)) ) )).

fof(t14_e_siec,axiom,(
    ! [A] :
      ( u1_struct_0(k6_e_siec(A)) = k1_tarski(A)
      & u1_e_siec(k6_e_siec(A)) = k1_xboole_0
      & u2_e_siec(k6_e_siec(A)) = k1_xboole_0 ) )).

fof(t15_e_siec,axiom,(
    ! [A,B] :
      ( v2_e_siec(g1_e_siec(k2_xboole_0(A,B),k6_relat_1(A),k6_relat_1(A)))
      & v3_e_siec(g1_e_siec(k2_xboole_0(A,B),k6_relat_1(A),k6_relat_1(A)))
      & l1_e_siec(g1_e_siec(k2_xboole_0(A,B),k6_relat_1(A),k6_relat_1(A))) ) )).

fof(d9_e_siec,axiom,(
    ! [A,B] : k7_e_siec(A,B) = g1_e_siec(k2_xboole_0(A,B),k6_relat_1(A),k6_relat_1(A)) )).

fof(t16_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k4_xboole_0(u1_e_siec(A),k6_relat_1(k1_relat_1(u1_e_siec(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u2_e_siec(A),k6_relat_1(k1_relat_1(u2_e_siec(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u1_e_siec(A),k6_relat_1(k2_relat_1(u1_e_siec(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k4_xboole_0(u2_e_siec(A),k6_relat_1(k2_relat_1(u2_e_siec(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))) ) ) )).

fof(t17_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k1_sysrel(u1_e_siec(A)) = k1_sysrel(u2_e_siec(A)) ) )).

fof(t18_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k2_relat_1(u1_e_siec(A)) = k2_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k1_relat_1(k1_sysrel(u1_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k2_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u2_e_siec(A)) = k1_relat_1(k1_sysrel(u2_e_siec(A)))
        & k2_relat_1(u1_e_siec(A)) = k2_relat_1(u2_e_siec(A)) ) ) )).

fof(t19_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k1_relat_1(u1_e_siec(A)),u1_struct_0(A))
        & r1_tarski(k2_relat_1(u1_e_siec(A)),u1_struct_0(A))
        & r1_tarski(k1_relat_1(u2_e_siec(A)),u1_struct_0(A))
        & r1_tarski(k2_relat_1(u2_e_siec(A)),u1_struct_0(A)) ) ) )).

fof(t20_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(u1_e_siec(A),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(u2_e_siec(A),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) )).

fof(t21_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) )).

fof(d10_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k8_e_siec(A) = k2_relat_1(u1_e_siec(A)) ) )).

fof(d11_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k9_e_siec(A) = k4_xboole_0(u1_struct_0(A),k8_e_siec(A)) ) )).

fof(t22_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => r1_xboole_0(k8_e_siec(A),k9_e_siec(A)) ) )).

fof(t23_e_siec,axiom,(
    ! [A,B,C] :
      ( ( v2_e_siec(C)
        & v3_e_siec(C)
        & l1_e_siec(C) )
     => ~ ( ( r2_hidden(k4_tarski(A,B),u1_e_siec(C))
            | r2_hidden(k4_tarski(A,B),u2_e_siec(C)) )
          & A != B
          & ~ ( r2_hidden(A,k9_e_siec(C))
              & r2_hidden(B,k8_e_siec(C)) ) ) ) )).

fof(t24_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k2_zfmisc_1(k9_e_siec(A),k8_e_siec(A)))
        & r1_tarski(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k2_zfmisc_1(k9_e_siec(A),k8_e_siec(A))) ) ) )).

fof(d12_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k10_e_siec(A) = k4_xboole_0(k2_xboole_0(k4_relat_1(u1_e_siec(A)),u2_e_siec(A)),k6_relat_1(u1_struct_0(A))) ) )).

fof(t25_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => r1_tarski(k10_e_siec(A),k2_xboole_0(k2_zfmisc_1(k8_e_siec(A),k9_e_siec(A)),k2_zfmisc_1(k9_e_siec(A),k8_e_siec(A)))) ) )).

fof(d13_e_siec,axiom,(
    $true )).

fof(d14_e_siec,axiom,(
    $true )).

fof(d15_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k11_e_siec(A) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))) ) )).

fof(d16_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k12_e_siec(A) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))) ) )).

fof(t26_e_siec,axiom,(
    $true )).

fof(t27_e_siec,axiom,(
    $true )).

fof(t28_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k11_e_siec(A),k2_zfmisc_1(k9_e_siec(A),k8_e_siec(A)))
        & r1_tarski(k12_e_siec(A),k2_zfmisc_1(k9_e_siec(A),k8_e_siec(A))) ) ) )).

fof(d17_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k13_e_siec(A) = u1_struct_0(A) ) )).

fof(d18_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k14_e_siec(A) = k4_relat_1(k2_xboole_0(u1_e_siec(A),u2_e_siec(A))) ) )).

fof(d19_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k15_e_siec(A) = k2_xboole_0(k2_xboole_0(k4_relat_1(u1_e_siec(A)),u2_e_siec(A)),k6_relat_1(u1_struct_0(A))) ) )).

fof(t29_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k14_e_siec(A),k2_zfmisc_1(k13_e_siec(A),k13_e_siec(A)))
        & r1_tarski(k15_e_siec(A),k2_zfmisc_1(k13_e_siec(A),k13_e_siec(A))) ) ) )).

fof(t30_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k14_e_siec(A),k14_e_siec(A)) = k14_e_siec(A)
        & k5_relat_1(k4_xboole_0(k14_e_siec(A),k6_relat_1(k13_e_siec(A))),k14_e_siec(A)) = k1_xboole_0
        & k2_xboole_0(k2_xboole_0(k14_e_siec(A),k4_relat_1(k14_e_siec(A))),k6_relat_1(k13_e_siec(A))) = k2_xboole_0(k15_e_siec(A),k4_relat_1(k15_e_siec(A))) ) ) )).

fof(t31_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))
        & k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))) ) ) )).

fof(t32_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) = k1_xboole_0 ) ) )).

fof(t33_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))))) = k1_xboole_0
        & k5_relat_1(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))))) = k1_xboole_0 ) ) )).

fof(t34_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))))) = k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))))
        & k5_relat_1(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k4_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))))) = k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) ) ) )).

fof(t35_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A))))) = k1_xboole_0
        & k5_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A))))) = k1_xboole_0 ) ) )).

fof(t36_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A)))),k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A))))) = k1_xboole_0
        & k5_relat_1(k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A)))),k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A))))) = k1_xboole_0 ) ) )).

fof(d20_e_siec,axiom,(
    $true )).

fof(d21_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k16_e_siec(A) = k2_xboole_0(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u2_e_siec(A))))) ) )).

fof(d22_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k17_e_siec(A) = k2_xboole_0(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A))))) ) )).

fof(t37_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k16_e_siec(A),k16_e_siec(A)) = k16_e_siec(A)
        & k5_relat_1(k16_e_siec(A),k17_e_siec(A)) = k16_e_siec(A)
        & k5_relat_1(k17_e_siec(A),k16_e_siec(A)) = k17_e_siec(A)
        & k5_relat_1(k17_e_siec(A),k17_e_siec(A)) = k17_e_siec(A) ) ) )).

fof(t38_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k16_e_siec(A),k4_xboole_0(k16_e_siec(A),k6_relat_1(k13_e_siec(A)))) = k1_xboole_0
        & k5_relat_1(k17_e_siec(A),k4_xboole_0(k17_e_siec(A),k6_relat_1(k13_e_siec(A)))) = k1_xboole_0 ) ) )).

fof(d23_e_siec,axiom,(
    $true )).

fof(d24_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => k18_e_siec(A) = k2_xboole_0(k4_xboole_0(k2_xboole_0(u1_e_siec(A),u2_e_siec(A)),k6_relat_1(u1_struct_0(A))),k6_relat_1(k4_xboole_0(u1_struct_0(A),k2_relat_1(u1_e_siec(A))))) ) )).

fof(t39_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k18_e_siec(A),k2_zfmisc_1(k13_e_siec(A),k13_e_siec(A)))
        & r1_tarski(k15_e_siec(A),k2_zfmisc_1(k13_e_siec(A),k13_e_siec(A))) ) ) )).

fof(t40_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( k5_relat_1(k18_e_siec(A),k18_e_siec(A)) = k18_e_siec(A)
        & k5_relat_1(k4_xboole_0(k18_e_siec(A),k6_relat_1(k13_e_siec(A))),k18_e_siec(A)) = k1_xboole_0
        & k2_xboole_0(k2_xboole_0(k18_e_siec(A),k4_relat_1(k18_e_siec(A))),k6_relat_1(k13_e_siec(A))) = k2_xboole_0(k15_e_siec(A),k4_relat_1(k15_e_siec(A))) ) ) )).

fof(t41_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))),k2_zfmisc_1(k8_e_siec(A),k9_e_siec(A)))
        & r1_tarski(k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))),k2_zfmisc_1(k8_e_siec(A),k9_e_siec(A))) ) ) )).

fof(d25_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => k19_e_siec(A) = k4_relat_1(k4_xboole_0(u2_e_siec(A),k6_relat_1(u1_struct_0(A)))) ) )).

fof(d26_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => k20_e_siec(A) = k4_relat_1(k4_xboole_0(u1_e_siec(A),k6_relat_1(u1_struct_0(A)))) ) )).

fof(t42_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => ( r1_tarski(k20_e_siec(A),k2_zfmisc_1(k8_e_siec(A),k9_e_siec(A)))
        & r1_tarski(k19_e_siec(A),k2_zfmisc_1(k8_e_siec(A),k9_e_siec(A))) ) ) )).

fof(dt_l1_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_e_siec,axiom,(
    ? [A] : l1_e_siec(A) )).

fof(abstractness_v1_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => ( v1_e_siec(A)
       => A = g1_e_siec(u1_struct_0(A),u1_e_siec(A),u2_e_siec(A)) ) ) )).

fof(dt_k1_e_siec,axiom,(
    $true )).

fof(dt_k2_e_siec,axiom,
    ( v1_e_siec(k2_e_siec)
    & v2_e_siec(k2_e_siec)
    & v3_e_siec(k2_e_siec)
    & l1_e_siec(k2_e_siec) )).

fof(dt_k3_e_siec,axiom,(
    ! [A] :
      ( v1_e_siec(k3_e_siec(A))
      & v2_e_siec(k3_e_siec(A))
      & v3_e_siec(k3_e_siec(A))
      & l1_e_siec(k3_e_siec(A)) ) )).

fof(dt_k4_e_siec,axiom,(
    ! [A] :
      ( v1_e_siec(k4_e_siec(A))
      & v2_e_siec(k4_e_siec(A))
      & v3_e_siec(k4_e_siec(A))
      & l1_e_siec(k4_e_siec(A)) ) )).

fof(dt_k5_e_siec,axiom,(
    ! [A] :
      ( v1_e_siec(k5_e_siec(A))
      & v2_e_siec(k5_e_siec(A))
      & v3_e_siec(k5_e_siec(A))
      & l1_e_siec(k5_e_siec(A)) ) )).

fof(dt_k6_e_siec,axiom,(
    ! [A] :
      ( v1_e_siec(k6_e_siec(A))
      & v2_e_siec(k6_e_siec(A))
      & v3_e_siec(k6_e_siec(A))
      & l1_e_siec(k6_e_siec(A)) ) )).

fof(dt_k7_e_siec,axiom,(
    ! [A,B] :
      ( v1_e_siec(k7_e_siec(A,B))
      & v2_e_siec(k7_e_siec(A,B))
      & v3_e_siec(k7_e_siec(A,B))
      & l1_e_siec(k7_e_siec(A,B)) ) )).

fof(dt_k8_e_siec,axiom,(
    $true )).

fof(dt_k9_e_siec,axiom,(
    $true )).

fof(dt_k10_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k10_e_siec(A)) ) )).

fof(dt_k11_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k11_e_siec(A)) ) )).

fof(dt_k12_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k12_e_siec(A)) ) )).

fof(dt_k13_e_siec,axiom,(
    $true )).

fof(dt_k14_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k14_e_siec(A)) ) )).

fof(dt_k15_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k15_e_siec(A)) ) )).

fof(dt_k16_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k16_e_siec(A)) ) )).

fof(dt_k17_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k17_e_siec(A)) ) )).

fof(dt_k18_e_siec,axiom,(
    ! [A] :
      ( ( v2_e_siec(A)
        & v3_e_siec(A)
        & l1_e_siec(A) )
     => v1_relat_1(k18_e_siec(A)) ) )).

fof(dt_k19_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => v1_relat_1(k19_e_siec(A)) ) )).

fof(dt_k20_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => v1_relat_1(k20_e_siec(A)) ) )).

fof(dt_u1_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => v1_relat_1(u1_e_siec(A)) ) )).

fof(dt_u2_e_siec,axiom,(
    ! [A] :
      ( l1_e_siec(A)
     => v1_relat_1(u2_e_siec(A)) ) )).

fof(dt_g1_e_siec,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ( v1_e_siec(g1_e_siec(A,B,C))
        & l1_e_siec(g1_e_siec(A,B,C)) ) ) )).

fof(free_g1_e_siec,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(B)
        & v1_relat_1(C) )
     => ! [D,E,F] :
          ( g1_e_siec(A,B,C) = g1_e_siec(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------