SET007 Axioms: SET007+329.ax
%------------------------------------------------------------------------------
% File : SET007+329 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 356 ( 93 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 261 ( 4 ~; 1 |; 191 &)
% ( 3 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 2 con; 0-3 aty)
% Number of variables : 97 ( 92 !; 5 ?)
% 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 ) ) ) ).
%------------------------------------------------------------------------------