SET007 Axioms: SET007+359.ax
%------------------------------------------------------------------------------
% File : SET007+359 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Basic Petri Net Concepts
% 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 : petri [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 84 ( 2 unt; 0 def)
% Number of atoms : 329 ( 56 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 278 ( 33 ~; 0 |; 112 &)
% ( 21 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 41 ( 41 usr; 1 con; 0-4 aty)
% Number of variables : 204 ( 173 !; 31 ?)
% 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_petri,axiom,
? [A] :
( l1_petri(A)
& v1_petri(A) ) ).
fof(rc2_petri,axiom,
? [A] :
( l1_petri(A)
& v3_petri(A) ) ).
fof(rc3_petri,axiom,
? [A] :
( l1_petri(A)
& v5_petri(A) ) ).
fof(t2_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ! [C] :
( r2_hidden(C,k5_petri(A,B))
<=> ? [D] :
( m1_petri(D,u2_petri(A),u1_petri(A),u4_petri(A))
& ? [E] :
( m1_subset_1(E,u1_petri(A))
& r2_hidden(E,B)
& D = k4_tarski(C,E) ) ) ) ) ) ).
fof(t4_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ! [C] :
( r2_hidden(C,k6_petri(A,B))
<=> ? [D] :
( m1_petri(D,u1_petri(A),u2_petri(A),u3_petri(A))
& ? [E] :
( m1_subset_1(E,u1_petri(A))
& r2_hidden(E,B)
& D = k4_tarski(E,C) ) ) ) ) ) ).
fof(t6_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> ! [C] :
( r2_hidden(C,k7_petri(A,B))
<=> ? [D] :
( m1_petri(D,u1_petri(A),u2_petri(A),u3_petri(A))
& ? [E] :
( m1_subset_1(E,u2_petri(A))
& r2_hidden(E,B)
& D = k4_tarski(C,E) ) ) ) ) ) ).
fof(t8_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> ! [C] :
( r2_hidden(C,k8_petri(A,B))
<=> ? [D] :
( m1_petri(D,u2_petri(A),u1_petri(A),u4_petri(A))
& ? [E] :
( m1_subset_1(E,u2_petri(A))
& r2_hidden(E,B)
& D = k4_tarski(E,C) ) ) ) ) ) ).
fof(t9_petri,axiom,
! [A] :
( l1_petri(A)
=> k5_petri(A,k1_subset_1(u1_petri(A))) = k1_xboole_0 ) ).
fof(t10_petri,axiom,
! [A] :
( l1_petri(A)
=> k6_petri(A,k1_subset_1(u1_petri(A))) = k1_xboole_0 ) ).
fof(t11_petri,axiom,
! [A] :
( l1_petri(A)
=> k7_petri(A,k1_subset_1(u2_petri(A))) = k1_xboole_0 ) ).
fof(t12_petri,axiom,
! [A] :
( l1_petri(A)
=> k8_petri(A,k1_subset_1(u2_petri(A))) = k1_xboole_0 ) ).
fof(d5_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ( v2_petri(B,A)
<=> m1_subset_1(k5_petri(A,B),k1_zfmisc_1(k6_petri(A,B))) ) ) ) ).
fof(d6_petri,axiom,
! [A] :
( l1_petri(A)
=> ( v3_petri(A)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
& v2_petri(B,A) ) ) ) ).
fof(d7_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ( v4_petri(B,A)
<=> m1_subset_1(k6_petri(A,B),k1_zfmisc_1(k5_petri(A,B))) ) ) ) ).
fof(d8_petri,axiom,
! [A] :
( l1_petri(A)
=> ( v5_petri(A)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
& v4_petri(B,A) ) ) ) ).
fof(d9_petri,axiom,
! [A] :
( l1_petri(A)
=> k10_petri(A) = g1_petri(u1_petri(A),u2_petri(A),k9_petri(u2_petri(A),u1_petri(A),u4_petri(A)),k9_petri(u1_petri(A),u2_petri(A),u3_petri(A))) ) ).
fof(t13_petri,axiom,
! [A] :
( l1_petri(A)
=> k10_petri(k10_petri(A)) = g1_petri(u1_petri(A),u2_petri(A),u3_petri(A),u4_petri(A)) ) ).
fof(t14_petri,axiom,
! [A] :
( l1_petri(A)
=> ( u1_petri(A) = u1_petri(k10_petri(A))
& u2_petri(A) = u2_petri(k10_petri(A))
& k9_petri(u1_petri(A),u2_petri(A),u3_petri(A)) = u4_petri(k10_petri(A))
& k9_petri(u2_petri(A),u1_petri(A),u4_petri(A)) = u3_petri(k10_petri(A)) ) ) ).
fof(d10_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k11_petri(A,B) = B ) ) ).
fof(d11_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u1_petri(A))
=> k12_petri(A,B) = B ) ) ).
fof(d12_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(k10_petri(A))))
=> k13_petri(A,B) = B ) ) ).
fof(d13_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u1_petri(k10_petri(A)))
=> k14_petri(A,B) = B ) ) ).
fof(d14_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> k15_petri(A,B) = B ) ) ).
fof(d15_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u2_petri(A))
=> k16_petri(A,B) = B ) ) ).
fof(d16_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(k10_petri(A))))
=> k17_petri(A,B) = B ) ) ).
fof(d17_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u2_petri(k10_petri(A)))
=> k18_petri(A,B) = B ) ) ).
fof(t15_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k6_petri(k10_petri(A),k11_petri(A,B)) = k5_petri(A,B) ) ) ).
fof(t16_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k5_petri(k10_petri(A),k11_petri(A,B)) = k6_petri(A,B) ) ) ).
fof(t17_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ( v2_petri(B,A)
<=> v4_petri(k11_petri(A,B),k10_petri(A)) ) ) ) ).
fof(t18_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> ( v4_petri(B,A)
<=> v2_petri(k11_petri(A,B),k10_petri(A)) ) ) ) ).
fof(t19_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u2_petri(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_petri(A)))
=> ( r2_hidden(B,k6_petri(A,C))
<=> ~ r1_xboole_0(k7_petri(A,k6_domain_1(u2_petri(A),B)),C) ) ) ) ) ).
fof(t20_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,u2_petri(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_petri(A)))
=> ( r2_hidden(B,k5_petri(A,C))
<=> ~ r1_xboole_0(k8_petri(A,k6_domain_1(u2_petri(A),B)),C) ) ) ) ) ).
fof(dt_m1_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> ! [D] :
( m1_petri(D,A,B,C)
=> m1_subset_1(D,k2_zfmisc_1(A,B)) ) ) ).
fof(existence_m1_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> ? [D] : m1_petri(D,A,B,C) ) ).
fof(redefinition_m1_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> ! [D] :
( m1_petri(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_l1_petri,axiom,
$true ).
fof(existence_l1_petri,axiom,
? [A] : l1_petri(A) ).
fof(abstractness_v1_petri,axiom,
! [A] :
( l1_petri(A)
=> ( v1_petri(A)
=> A = g1_petri(u1_petri(A),u2_petri(A),u3_petri(A),u4_petri(A)) ) ) ).
fof(dt_k1_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u3_petri(A)) )
=> m1_subset_1(k1_petri(A,B),u1_petri(A)) ) ).
fof(redefinition_k1_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u3_petri(A)) )
=> k1_petri(A,B) = k1_mcart_1(B) ) ).
fof(dt_k2_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u3_petri(A)) )
=> m1_subset_1(k2_petri(A,B),u2_petri(A)) ) ).
fof(redefinition_k2_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u3_petri(A)) )
=> k2_petri(A,B) = k2_mcart_1(B) ) ).
fof(dt_k3_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u4_petri(A)) )
=> m1_subset_1(k3_petri(A,B),u2_petri(A)) ) ).
fof(redefinition_k3_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u4_petri(A)) )
=> k3_petri(A,B) = k1_mcart_1(B) ) ).
fof(dt_k4_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u4_petri(A)) )
=> m1_subset_1(k4_petri(A,B),u1_petri(A)) ) ).
fof(redefinition_k4_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u4_petri(A)) )
=> k4_petri(A,B) = k2_mcart_1(B) ) ).
fof(dt_k5_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
=> m1_subset_1(k5_petri(A,B),k1_zfmisc_1(u2_petri(A))) ) ).
fof(dt_k6_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
=> m1_subset_1(k6_petri(A,B),k1_zfmisc_1(u2_petri(A))) ) ).
fof(dt_k7_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u2_petri(A))) )
=> m1_subset_1(k7_petri(A,B),k1_zfmisc_1(u1_petri(A))) ) ).
fof(dt_k8_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u2_petri(A))) )
=> m1_subset_1(k8_petri(A,B),k1_zfmisc_1(u1_petri(A))) ) ).
fof(dt_k9_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> ( ~ v1_xboole_0(k9_petri(A,B,C))
& m2_relset_1(k9_petri(A,B,C),B,A) ) ) ).
fof(involutiveness_k9_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> k9_petri(A,B,k9_petri(A,B,C)) = C ) ).
fof(redefinition_k9_petri,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B) )
=> k9_petri(A,B,C) = k4_relat_1(C) ) ).
fof(dt_k10_petri,axiom,
! [A] :
( l1_petri(A)
=> ( v1_petri(k10_petri(A))
& l1_petri(k10_petri(A)) ) ) ).
fof(dt_k11_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
=> m1_subset_1(k11_petri(A,B),k1_zfmisc_1(u1_petri(k10_petri(A)))) ) ).
fof(dt_k12_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u1_petri(A)) )
=> m1_subset_1(k12_petri(A,B),u1_petri(k10_petri(A))) ) ).
fof(dt_k13_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u1_petri(k10_petri(A)))) )
=> m1_subset_1(k13_petri(A,B),k1_zfmisc_1(u1_petri(A))) ) ).
fof(dt_k14_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u1_petri(k10_petri(A))) )
=> m1_subset_1(k14_petri(A,B),u1_petri(A)) ) ).
fof(dt_k15_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u2_petri(A))) )
=> m1_subset_1(k15_petri(A,B),k1_zfmisc_1(u2_petri(k10_petri(A)))) ) ).
fof(dt_k16_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u2_petri(A)) )
=> m1_subset_1(k16_petri(A,B),u2_petri(k10_petri(A))) ) ).
fof(dt_k17_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,k1_zfmisc_1(u2_petri(k10_petri(A)))) )
=> m1_subset_1(k17_petri(A,B),k1_zfmisc_1(u2_petri(A))) ) ).
fof(dt_k18_petri,axiom,
! [A,B] :
( ( l1_petri(A)
& m1_subset_1(B,u2_petri(k10_petri(A))) )
=> m1_subset_1(k18_petri(A,B),u2_petri(A)) ) ).
fof(dt_u1_petri,axiom,
! [A] :
( l1_petri(A)
=> ~ v1_xboole_0(u1_petri(A)) ) ).
fof(dt_u2_petri,axiom,
! [A] :
( l1_petri(A)
=> ~ v1_xboole_0(u2_petri(A)) ) ).
fof(dt_u3_petri,axiom,
! [A] :
( l1_petri(A)
=> ( ~ v1_xboole_0(u3_petri(A))
& m2_relset_1(u3_petri(A),u1_petri(A),u2_petri(A)) ) ) ).
fof(dt_u4_petri,axiom,
! [A] :
( l1_petri(A)
=> ( ~ v1_xboole_0(u4_petri(A))
& m2_relset_1(u4_petri(A),u2_petri(A),u1_petri(A)) ) ) ).
fof(dt_g1_petri,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B)
& ~ v1_xboole_0(D)
& m1_relset_1(D,B,A) )
=> ( v1_petri(g1_petri(A,B,C,D))
& l1_petri(g1_petri(A,B,C,D)) ) ) ).
fof(free_g1_petri,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_relset_1(C,A,B)
& ~ v1_xboole_0(D)
& m1_relset_1(D,B,A) )
=> ! [E,F,G,H] :
( g1_petri(A,B,C,D) = g1_petri(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(d1_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k5_petri(A,B) = a_2_0_petri(A,B) ) ) ).
fof(d2_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k6_petri(A,B) = a_2_1_petri(A,B) ) ) ).
fof(t1_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k5_petri(A,B) = a_2_2_petri(A,B) ) ) ).
fof(t3_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
=> k6_petri(A,B) = a_2_3_petri(A,B) ) ) ).
fof(d3_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> k7_petri(A,B) = a_2_4_petri(A,B) ) ) ).
fof(d4_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> k8_petri(A,B) = a_2_5_petri(A,B) ) ) ).
fof(t5_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> k7_petri(A,B) = a_2_6_petri(A,B) ) ) ).
fof(t7_petri,axiom,
! [A] :
( l1_petri(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u2_petri(A)))
=> k8_petri(A,B) = a_2_7_petri(A,B) ) ) ).
fof(fraenkel_a_2_0_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
=> ( r2_hidden(A,a_2_0_petri(B,C))
<=> ? [D] :
( m1_subset_1(D,u2_petri(B))
& A = D
& ? [E] :
( m1_petri(E,u2_petri(B),u1_petri(B),u4_petri(B))
& ? [F] :
( m1_subset_1(F,u1_petri(B))
& r2_hidden(F,C)
& E = k1_domain_1(u2_petri(B),u1_petri(B),D,F) ) ) ) ) ) ).
fof(fraenkel_a_2_1_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
=> ( r2_hidden(A,a_2_1_petri(B,C))
<=> ? [D] :
( m1_subset_1(D,u2_petri(B))
& A = D
& ? [E] :
( m1_petri(E,u1_petri(B),u2_petri(B),u3_petri(B))
& ? [F] :
( m1_subset_1(F,u1_petri(B))
& r2_hidden(F,C)
& E = k1_domain_1(u1_petri(B),u2_petri(B),F,D) ) ) ) ) ) ).
fof(fraenkel_a_2_2_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
=> ( r2_hidden(A,a_2_2_petri(B,C))
<=> ? [D] :
( m1_petri(D,u2_petri(B),u1_petri(B),u4_petri(B))
& A = k3_petri(B,D)
& r2_hidden(k4_petri(B,D),C) ) ) ) ).
fof(fraenkel_a_2_3_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u1_petri(B))) )
=> ( r2_hidden(A,a_2_3_petri(B,C))
<=> ? [D] :
( m1_petri(D,u1_petri(B),u2_petri(B),u3_petri(B))
& A = k2_petri(B,D)
& r2_hidden(k1_petri(B,D),C) ) ) ) ).
fof(fraenkel_a_2_4_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u2_petri(B))) )
=> ( r2_hidden(A,a_2_4_petri(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_petri(B))
& A = D
& ? [E] :
( m1_petri(E,u1_petri(B),u2_petri(B),u3_petri(B))
& ? [F] :
( m1_subset_1(F,u2_petri(B))
& r2_hidden(F,C)
& E = k1_domain_1(u1_petri(B),u2_petri(B),D,F) ) ) ) ) ) ).
fof(fraenkel_a_2_5_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u2_petri(B))) )
=> ( r2_hidden(A,a_2_5_petri(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_petri(B))
& A = D
& ? [E] :
( m1_petri(E,u2_petri(B),u1_petri(B),u4_petri(B))
& ? [F] :
( m1_subset_1(F,u2_petri(B))
& r2_hidden(F,C)
& E = k1_domain_1(u2_petri(B),u1_petri(B),F,D) ) ) ) ) ) ).
fof(fraenkel_a_2_6_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u2_petri(B))) )
=> ( r2_hidden(A,a_2_6_petri(B,C))
<=> ? [D] :
( m1_petri(D,u1_petri(B),u2_petri(B),u3_petri(B))
& A = k1_petri(B,D)
& r2_hidden(k2_petri(B,D),C) ) ) ) ).
fof(fraenkel_a_2_7_petri,axiom,
! [A,B,C] :
( ( l1_petri(B)
& m1_subset_1(C,k1_zfmisc_1(u2_petri(B))) )
=> ( r2_hidden(A,a_2_7_petri(B,C))
<=> ? [D] :
( m1_petri(D,u2_petri(B),u1_petri(B),u4_petri(B))
& A = k4_petri(B,D)
& r2_hidden(k3_petri(B,D),C) ) ) ) ).
%------------------------------------------------------------------------------