SET007 Axioms: SET007+218.ax
%------------------------------------------------------------------------------
% File : SET007+218 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Kuratowski - Zorn Lemma
% 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 : orders_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 207 ( 112 unt; 0 def)
% Number of atoms : 882 ( 40 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 784 ( 109 ~; 4 |; 387 &)
% ( 27 <=>; 257 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 1 con; 0-3 aty)
% Number of variables : 271 ( 256 !; 15 ?)
% 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_orders_2,axiom,
? [A] :
( l1_orders_2(A)
& v1_orders_2(A) ) ).
fof(fc1_orders_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,A,A) )
=> ( ~ v3_struct_0(g1_orders_2(A,B))
& v1_orders_2(g1_orders_2(A,B)) ) ) ).
fof(rc2_orders_2,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A) ) ).
fof(fc2_orders_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(u1_orders_2(A))
& v1_relat_2(u1_orders_2(A))
& v4_relat_2(u1_orders_2(A))
& v8_relat_2(u1_orders_2(A))
& v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(fc3_orders_2,axiom,
! [A,B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A) )
=> ( v1_orders_2(g1_orders_2(A,B))
& v2_orders_2(g1_orders_2(A,B))
& v3_orders_2(g1_orders_2(A,B))
& v4_orders_2(g1_orders_2(A,B)) ) ) ).
fof(fc4_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_xboole_0(k1_pre_topc(A))
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A))
& v5_orders_2(k1_pre_topc(A),A) ) ) ).
fof(rc3_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v5_orders_2(B,A) ) ) ).
fof(fc5_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k4_orders_2(A,B)) ) ).
fof(d1_orders_2,axiom,
$true ).
fof(d2_orders_2,axiom,
$true ).
fof(d3_orders_2,axiom,
$true ).
fof(d4_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_orders_2(A)
<=> r1_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ).
fof(d5_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_orders_2(A)
<=> r8_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ).
fof(d6_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_orders_2(A)
<=> r4_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ).
fof(d7_orders_2,axiom,
$true ).
fof(d8_orders_2,axiom,
$true ).
fof(d9_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ).
fof(d10_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_orders_2(A,B,C)
<=> ( r1_orders_2(A,B,C)
& B != C ) ) ) ) ) ).
fof(t1_orders_2,axiom,
$true ).
fof(t2_orders_2,axiom,
$true ).
fof(t3_orders_2,axiom,
$true ).
fof(t4_orders_2,axiom,
$true ).
fof(t5_orders_2,axiom,
$true ).
fof(t6_orders_2,axiom,
$true ).
fof(t7_orders_2,axiom,
$true ).
fof(t8_orders_2,axiom,
$true ).
fof(t9_orders_2,axiom,
$true ).
fof(t10_orders_2,axiom,
$true ).
fof(t11_orders_2,axiom,
$true ).
fof(t12_orders_2,axiom,
$true ).
fof(t13_orders_2,axiom,
$true ).
fof(t14_orders_2,axiom,
$true ).
fof(t15_orders_2,axiom,
$true ).
fof(t16_orders_2,axiom,
$true ).
fof(t17_orders_2,axiom,
$true ).
fof(t18_orders_2,axiom,
$true ).
fof(t19_orders_2,axiom,
$true ).
fof(t20_orders_2,axiom,
$true ).
fof(t21_orders_2,axiom,
$true ).
fof(t22_orders_2,axiom,
$true ).
fof(t23_orders_2,axiom,
$true ).
fof(t24_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_orders_2(A,B,B) ) ) ).
fof(t25_orders_2,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,C)
& r1_orders_2(A,C,B) )
=> B = C ) ) ) ) ).
fof(t26_orders_2,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_orders_2(A,B,C)
& r1_orders_2(A,C,D) )
=> r1_orders_2(A,B,D) ) ) ) ) ) ).
fof(t27_orders_2,axiom,
$true ).
fof(t28_orders_2,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r2_orders_2(A,B,C)
& r2_orders_2(A,C,B) ) ) ) ) ).
fof(t29_orders_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_orders_2(A,B,C)
& r2_orders_2(A,C,D) )
=> r2_orders_2(A,B,D) ) ) ) ) ) ).
fof(t30_orders_2,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r1_orders_2(A,B,C)
& r2_orders_2(A,C,B) ) ) ) ) ).
fof(t31_orders_2,axiom,
$true ).
fof(t32_orders_2,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( ( r2_orders_2(A,B,C)
& r1_orders_2(A,C,D) )
| ( r1_orders_2(A,B,C)
& r2_orders_2(A,C,D) ) )
=> r2_orders_2(A,B,D) ) ) ) ) ) ).
fof(d11_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_orders_2(B,A)
<=> r7_relat_2(u1_orders_2(A),B) ) ) ) ).
fof(t33_orders_2,axiom,
$true ).
fof(t34_orders_2,axiom,
$true ).
fof(t35_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v5_orders_2(k1_struct_0(A,B),A)
& m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t36_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v5_orders_2(k2_struct_0(A,B,C),A)
& m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) )
<=> ( r3_orders_2(A,B,C)
| r3_orders_2(A,C,B) ) ) ) ) ) ).
fof(t37_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,B)
=> ( v5_orders_2(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t38_orders_2,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ ( ? [D] :
( v5_orders_2(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(B,D)
& r2_hidden(C,D) )
& ~ r1_orders_2(A,B,C)
& ~ r1_orders_2(A,C,B) )
& ~ ( ( r1_orders_2(A,B,C)
| r1_orders_2(A,C,B) )
& ! [D] :
( ( v5_orders_2(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(B,D)
& r2_hidden(C,D) ) ) ) ) ) ) ) ).
fof(t39_orders_2,axiom,
! [A] :
( ( v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ? [D] :
( v5_orders_2(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(B,D)
& r2_hidden(C,D) )
<=> ( r2_orders_2(A,B,C)
<=> ~ r1_orders_2(A,C,B) ) ) ) ) ) ).
fof(t40_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_wellord1(u1_orders_2(A),B)
=> ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t41_orders_2,axiom,
$true ).
fof(t42_orders_2,axiom,
$true ).
fof(t43_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> k1_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A) ) ).
fof(t44_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> k1_orders_2(A,k2_pre_topc(A)) = k1_xboole_0 ) ).
fof(t45_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> k2_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A) ) ).
fof(t46_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> k2_orders_2(A,k2_pre_topc(A)) = k1_xboole_0 ) ).
fof(t47_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(B,C)
& r2_hidden(B,k1_orders_2(A,C)) ) ) ) ) ).
fof(t48_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r2_hidden(B,k1_orders_2(A,k1_struct_0(A,B))) ) ) ).
fof(t49_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(B,C)
& r2_hidden(B,k2_orders_2(A,C)) ) ) ) ) ).
fof(t50_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))) ) ) ).
fof(t51_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_orders_2(A,B,C)
<=> r2_hidden(C,k1_orders_2(A,k1_struct_0(A,B))) ) ) ) ) ).
fof(t52_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_orders_2(A,B,C)
<=> r2_hidden(B,k2_orders_2(A,k1_struct_0(A,C))) ) ) ) ) ).
fof(d14_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_orders_2(A,B,C) = k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B) ) ) ) ).
fof(d15_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B != k1_xboole_0
=> ( m1_orders_2(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(D,B)
& C = k3_orders_2(A,B,D) ) ) )
& ( B = k1_xboole_0
=> ( m1_orders_2(C,A,B)
<=> C = k1_xboole_0 ) ) ) ) ) ) ).
fof(t53_orders_2,axiom,
$true ).
fof(t54_orders_2,axiom,
$true ).
fof(t55_orders_2,axiom,
$true ).
fof(t56_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,k3_orders_2(B,D,C))
<=> ( r2_hidden(A,k2_orders_2(B,k1_struct_0(B,C)))
& r2_hidden(A,D) ) ) ) ) ) ).
fof(t57_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k3_orders_2(A,D,C))
<=> ( r2_orders_2(A,B,C)
& r2_hidden(B,D) ) ) ) ) ) ) ).
fof(t58_orders_2,axiom,
$true ).
fof(t59_orders_2,axiom,
$true ).
fof(t60_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_orders_2(A,k1_pre_topc(A),B) = k1_xboole_0 ) ) ).
fof(t61_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k3_orders_2(A,C,B),C) ) ) ) ).
fof(t62_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ r2_hidden(B,k3_orders_2(A,C,B)) ) ) ) ).
fof(t63_orders_2,axiom,
$true ).
fof(t64_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_orders_2(A,B,C)
=> r1_tarski(k3_orders_2(A,D,B),k3_orders_2(A,D,C)) ) ) ) ) ) ).
fof(t65_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,D)
=> r1_tarski(k3_orders_2(A,C,B),k3_orders_2(A,D,B)) ) ) ) ) ) ).
fof(t66_orders_2,axiom,
$true ).
fof(t67_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_orders_2(C,A,B)
=> r1_tarski(C,B) ) ) ) ).
fof(t68_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ~ ( B != k1_xboole_0
& m1_orders_2(B,A,B) )
& ~ ( ~ m1_orders_2(B,A,B)
& B = k1_xboole_0 ) ) ) ) ).
fof(t69_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( ~ ( B = k1_xboole_0
& C = k1_xboole_0 )
& m1_orders_2(B,A,C)
& m1_orders_2(C,A,B) ) ) ) ) ).
fof(t70_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_orders_2(A,B,C)
& r2_hidden(B,D)
& r2_hidden(C,E)
& m1_orders_2(E,A,D) )
=> r2_hidden(B,E) ) ) ) ) ) ) ).
fof(t71_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(B,C)
& m1_orders_2(C,A,D) )
=> k3_orders_2(A,C,B) = k3_orders_2(A,D,B) ) ) ) ) ) ).
fof(t72_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(B,C)
& r2_wellord1(u1_orders_2(A),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_orders_2(A,D,E) )
=> r2_hidden(D,B) ) ) )
& B != C
& ~ m1_orders_2(B,A,C) ) ) ) ) ).
fof(t73_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(B,C)
& r2_wellord1(u1_orders_2(A),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(E,B)
& r2_hidden(D,C)
& r2_orders_2(A,D,E) )
=> r2_hidden(D,B) ) ) )
& B != C
& ~ m1_orders_2(B,A,C) ) ) ) ) ).
fof(d16_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( ( v5_orders_2(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m2_orders_2(C,A,B)
<=> ( C != k1_xboole_0
& r2_wellord1(u1_orders_2(A),C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D))) = D ) ) ) ) ) ) ) ).
fof(t74_orders_2,axiom,
$true ).
fof(t75_orders_2,axiom,
$true ).
fof(t76_orders_2,axiom,
$true ).
fof(t77_orders_2,axiom,
$true ).
fof(t78_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> m2_orders_2(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B) ) ) ).
fof(t79_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( m2_orders_2(C,A,B)
=> r2_hidden(k1_funct_1(B,u1_struct_0(A)),C) ) ) ) ).
fof(t80_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_orders_1(D,k1_orders_1(u1_struct_0(A)))
=> ! [E] :
( m2_orders_2(E,A,D)
=> ( ( r2_hidden(B,E)
& C = k1_funct_1(D,u1_struct_0(A)) )
=> r3_orders_2(A,C,B) ) ) ) ) ) ) ).
fof(t81_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_orders_1(C,k1_orders_1(u1_struct_0(A)))
=> ! [D] :
( m2_orders_2(D,A,C)
=> ( B = k1_funct_1(C,u1_struct_0(A))
=> k3_orders_2(A,D,B) = k1_xboole_0 ) ) ) ) ) ).
fof(t82_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( m2_orders_2(C,A,B)
=> ! [D] :
( m2_orders_2(D,A,B)
=> ~ r1_xboole_0(C,D) ) ) ) ) ).
fof(t83_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( m2_orders_2(C,A,B)
=> ! [D] :
( m2_orders_2(D,A,B)
=> ( C != D
=> ( m1_orders_2(C,A,D)
<=> ~ m1_orders_2(D,A,C) ) ) ) ) ) ) ).
fof(t84_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( m2_orders_2(C,A,B)
=> ! [D] :
( m2_orders_2(D,A,B)
=> ( r2_xboole_0(C,D)
<=> m1_orders_2(C,A,D) ) ) ) ) ) ).
fof(d17_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> ! [C] :
( C = k4_orders_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m2_orders_2(D,A,B) ) ) ) ) ).
fof(t85_orders_2,axiom,
$true ).
fof(t86_orders_2,axiom,
$true ).
fof(t87_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> k3_tarski(k4_orders_2(A,B)) != k1_xboole_0 ) ) ).
fof(t88_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_orders_1(C,k1_orders_1(u1_struct_0(A)))
=> ! [D] :
( m2_orders_2(D,A,C)
=> ( B = k3_tarski(k4_orders_2(A,C))
=> ( D = k3_tarski(k4_orders_2(A,C))
| m1_orders_2(D,A,B) ) ) ) ) ) ) ).
fof(t89_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_orders_1(B,k1_orders_1(u1_struct_0(A)))
=> m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B) ) ) ).
fof(t90_orders_2,axiom,
$true ).
fof(t91_orders_2,axiom,
$true ).
fof(t92_orders_2,axiom,
$true ).
fof(t93_orders_2,axiom,
$true ).
fof(t94_orders_2,axiom,
$true ).
fof(t95_orders_2,axiom,
$true ).
fof(t96_orders_2,axiom,
$true ).
fof(t97_orders_2,axiom,
$true ).
fof(t98_orders_2,axiom,
$true ).
fof(t99_orders_2,axiom,
$true ).
fof(t100_orders_2,axiom,
$true ).
fof(t101_orders_2,axiom,
$true ).
fof(t102_orders_2,axiom,
$true ).
fof(t103_orders_2,axiom,
$true ).
fof(t104_orders_2,axiom,
$true ).
fof(t105_orders_2,axiom,
$true ).
fof(t106_orders_2,axiom,
$true ).
fof(t107_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k3_relat_1(k2_wellord1(u1_orders_2(A),B)) = B ) ) ).
fof(t108_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_orders_1(k2_wellord1(u1_orders_2(A),B))
=> ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t109_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_orders_1(k2_wellord1(u1_orders_2(A),B)) ) ) ).
fof(t110_orders_2,axiom,
$true ).
fof(t111_orders_2,axiom,
$true ).
fof(t112_orders_2,axiom,
$true ).
fof(t113_orders_2,axiom,
$true ).
fof(t114_orders_2,axiom,
$true ).
fof(t115_orders_2,axiom,
$true ).
fof(t116_orders_2,axiom,
$true ).
fof(t117_orders_2,axiom,
$true ).
fof(t118_orders_2,axiom,
$true ).
fof(t119_orders_2,axiom,
$true ).
fof(t120_orders_2,axiom,
$true ).
fof(t121_orders_2,axiom,
$true ).
fof(t122_orders_2,axiom,
$true ).
fof(t123_orders_2,axiom,
$true ).
fof(t124_orders_2,axiom,
$true ).
fof(t125_orders_2,axiom,
$true ).
fof(t126_orders_2,axiom,
$true ).
fof(t127_orders_2,axiom,
$true ).
fof(t128_orders_2,axiom,
$true ).
fof(t129_orders_2,axiom,
$true ).
fof(t130_orders_2,axiom,
$true ).
fof(t131_orders_2,axiom,
$true ).
fof(t132_orders_2,axiom,
$true ).
fof(t133_orders_2,axiom,
$true ).
fof(t134_orders_2,axiom,
$true ).
fof(t135_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r3_orders_1(u1_orders_2(A),B)
=> ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t136_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_orders_1(u1_orders_2(A),B) ) ) ).
fof(t137_orders_2,axiom,
$true ).
fof(t138_orders_2,axiom,
$true ).
fof(t139_orders_2,axiom,
$true ).
fof(t140_orders_2,axiom,
$true ).
fof(t141_orders_2,axiom,
$true ).
fof(t142_orders_2,axiom,
$true ).
fof(t143_orders_2,axiom,
$true ).
fof(t144_orders_2,axiom,
$true ).
fof(t145_orders_2,axiom,
$true ).
fof(t146_orders_2,axiom,
$true ).
fof(t147_orders_2,axiom,
$true ).
fof(t148_orders_2,axiom,
$true ).
fof(t149_orders_2,axiom,
$true ).
fof(t150_orders_2,axiom,
$true ).
fof(t151_orders_2,axiom,
$true ).
fof(t152_orders_2,axiom,
$true ).
fof(t153_orders_2,axiom,
$true ).
fof(t154_orders_2,axiom,
$true ).
fof(t155_orders_2,axiom,
$true ).
fof(t156_orders_2,axiom,
$true ).
fof(t157_orders_2,axiom,
$true ).
fof(t158_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r7_orders_1(u1_orders_2(A),B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r2_orders_2(A,C,B) ) ) ) ) ).
fof(t159_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r6_orders_1(u1_orders_2(A),B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r2_orders_2(A,B,C) ) ) ) ) ).
fof(t160_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r8_orders_1(u1_orders_2(A),B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != C
=> r2_orders_2(A,C,B) ) ) ) ) ) ).
fof(t161_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r9_orders_1(u1_orders_2(A),B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != C
=> r2_orders_2(A,B,C) ) ) ) ) ) ).
fof(t162_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ~ ( ! [B] :
( ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r3_orders_2(A,D,C) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_orders_2(A,B,C) ) ) ) ) ).
fof(t163_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ~ ( ! [B] :
( ( v5_orders_2(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,B)
=> r3_orders_2(A,C,D) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_orders_2(A,C,B) ) ) ) ) ).
fof(dt_m1_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_orders_2(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] : m1_orders_2(C,A,B) ) ).
fof(dt_m2_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
=> ! [C] :
( m2_orders_2(C,A,B)
=> ( v5_orders_2(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(existence_m2_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_orders_1(B,k1_orders_1(u1_struct_0(A))) )
=> ? [C] : m2_orders_2(C,A,B) ) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_orders_2,axiom,
? [A] : l1_orders_2(A) ).
fof(abstractness_v1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(A)
=> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ).
fof(irreflexivity_r2_orders_2,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ r2_orders_2(A,B,B) ) ).
fof(reflexivity_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_orders_2(A,B,B) ) ).
fof(redefinition_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_orders_2(A,B,C)
<=> r1_orders_2(A,B,C) ) ) ).
fof(dt_k1_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_orders_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k3_orders_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_orders_2,axiom,
$true ).
fof(dt_u1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( v1_orders_2(g1_orders_2(A,B))
& l1_orders_2(g1_orders_2(A,B)) ) ) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ! [C,D] :
( g1_orders_2(A,B) = g1_orders_2(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(d12_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_orders_2(A,B) = a_2_0_orders_2(A,B) ) ) ).
fof(d13_orders_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_orders_2(A,B) = a_2_1_orders_2(A,B) ) ) ).
fof(fraenkel_a_2_0_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_orders_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,C)
=> r2_orders_2(B,E,D) ) ) ) ) ) ).
fof(fraenkel_a_2_1_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_1_orders_2(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,C)
=> r2_orders_2(B,D,E) ) ) ) ) ) ).
%------------------------------------------------------------------------------