SET007 Axioms: SET007+493.ax
%------------------------------------------------------------------------------
% File : SET007+493 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Moore-Smith Convergence
% 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 : yellow_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 154 ( 10 unt; 0 def)
% Number of atoms : 1133 ( 51 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1190 ( 211 ~; 2 |; 592 &)
% ( 39 <=>; 346 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 70 ( 68 usr; 1 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 1 con; 0-5 aty)
% Number of variables : 432 ( 405 !; 27 ?)
% 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_yellow_6,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A) ) ).
fof(cc1_yellow_6,axiom,
! [A] :
( v1_classes2(A)
=> ( v1_ordinal1(A)
& v1_classes1(A)
& v2_classes1(A)
& v1_classes2(A) ) ) ).
fof(cc2_yellow_6,axiom,
! [A] :
( ( v1_ordinal1(A)
& v2_classes1(A) )
=> ( v1_ordinal1(A)
& v1_classes1(A)
& v2_classes1(A)
& v1_classes2(A) ) ) ).
fof(fc1_yellow_6,axiom,
! [A] :
( v1_ordinal1(k2_yellow_6(A))
& v1_classes1(k2_yellow_6(A))
& v2_classes1(k2_yellow_6(A))
& v1_classes2(k2_yellow_6(A)) ) ).
fof(fc2_yellow_6,axiom,
! [A] :
( ~ v1_xboole_0(k2_yellow_6(A))
& v1_ordinal1(k2_yellow_6(A))
& v1_classes1(k2_yellow_6(A))
& v2_classes1(k2_yellow_6(A))
& v1_classes2(k2_yellow_6(A)) ) ).
fof(rc2_yellow_6,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A)
& v2_pralg_1(A) ) ).
fof(fc3_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v5_seqm_3(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B)) ) ) ).
fof(rc3_yellow_6,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v4_waybel_3(B) ) ).
fof(fc4_yellow_6,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_yellow_1(B)
& m1_pboole(B,A) )
=> v1_fraenkel(u1_struct_0(k5_yellow_1(A,B))) ) ).
fof(fc5_yellow_6,axiom,
! [A,B] :
( ( v2_pralg_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( v1_relat_1(k12_pralg_1(A,B))
& v2_relat_1(k12_pralg_1(A,B))
& v1_funct_1(k12_pralg_1(A,B)) ) ) ).
fof(fc6_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v13_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(fc7_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v13_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v12_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(fc8_yellow_6,axiom,
! [A] :
( ~ v3_struct_0(k3_yellow_1(A))
& v1_orders_2(k3_yellow_1(A))
& v2_orders_2(k3_yellow_1(A))
& v3_orders_2(k3_yellow_1(A))
& v4_orders_2(k3_yellow_1(A))
& v1_yellow_0(k3_yellow_1(A))
& v2_yellow_0(k3_yellow_1(A))
& v3_yellow_0(k3_yellow_1(A))
& v7_waybel_0(k3_yellow_1(A))
& v24_waybel_0(k3_yellow_1(A))
& v25_waybel_0(k3_yellow_1(A))
& ~ v1_yellow_3(k3_yellow_1(A))
& v1_lattice3(k3_yellow_1(A))
& v2_lattice3(k3_yellow_1(A))
& v3_lattice3(k3_yellow_1(A)) ) ).
fof(rc4_yellow_6,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v3_orders_2(A)
& v7_waybel_0(A) ) ).
fof(rc5_yellow_6,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_yellow_1(B)
& v4_waybel_3(B) ) ).
fof(fc9_yellow_6,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k5_yellow_1(A,B))
& v1_orders_2(k5_yellow_1(A,B)) ) ) ).
fof(fc10_yellow_6,axiom,
! [A,B] :
( ( v7_waybel_0(A)
& l1_orders_2(A)
& v7_waybel_0(B)
& l1_orders_2(B) )
=> ( v1_orders_2(k3_yellow_3(A,B))
& v7_waybel_0(k3_yellow_3(A,B)) ) ) ).
fof(fc11_yellow_6,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v6_waybel_0(k4_yellow_6(A,B,C),B)
& v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ).
fof(fc12_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k4_yellow_6(A,B,C))
& v6_waybel_0(k4_yellow_6(A,B,C),B)
& v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ).
fof(fc13_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v7_waybel_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k4_yellow_6(A,B,C))
& v6_waybel_0(k4_yellow_6(A,B,C),B)
& v7_waybel_0(k4_yellow_6(A,B,C))
& v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ).
fof(fc14_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v3_struct_0(k4_yellow_6(A,B,C))
& v3_orders_2(k4_yellow_6(A,B,C))
& v6_waybel_0(k4_yellow_6(A,B,C),B)
& v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ).
fof(fc15_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ( ~ v1_xboole_0(u1_waybel_0(A,B))
& v1_relat_1(u1_waybel_0(A,B))
& v1_funct_1(u1_waybel_0(A,B))
& v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(rc6_yellow_6,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ? [C] :
( m1_yellow_6(C,A,B)
& v6_waybel_0(C,A)
& v2_yellow_6(C,A,B) ) ) ).
fof(rc7_yellow_6,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ? [C] :
( m1_yellow_6(C,A,B)
& ~ v3_struct_0(C)
& v6_waybel_0(C,A)
& v2_yellow_6(C,A,B) ) ) ).
fof(rc8_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v1_yellow_6(B,A) ) ) ).
fof(fc16_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ( v1_relat_1(u1_waybel_0(A,B))
& v1_funct_1(u1_waybel_0(A,B))
& v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A))
& v5_seqm_3(u1_waybel_0(A,B)) ) ) ).
fof(fc17_yellow_6,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v3_orders_2(B)
& l1_waybel_0(B,A) )
=> ( v3_orders_2(k6_yellow_6(A,B,C))
& v6_waybel_0(k6_yellow_6(A,B,C),A)
& v2_yellow_6(k6_yellow_6(A,B,C),A,B) ) ) ).
fof(fc18_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(k7_yellow_6(A)) ) ).
fof(cc3_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ! [C] :
( m3_yellow_6(C,A,B)
=> v1_yellow_1(C) ) ) ).
fof(cc4_yellow_6,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> ( ~ v1_xboole_0(C)
& v1_yellow_1(C)
& v4_waybel_3(C) ) ) ) ).
fof(fc19_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& m3_yellow_6(C,u1_struct_0(B),A) )
=> ( ~ v3_struct_0(k5_yellow_1(u1_struct_0(B),C))
& v1_orders_2(k5_yellow_1(u1_struct_0(B),C))
& v3_orders_2(k5_yellow_1(u1_struct_0(B),C))
& v7_waybel_0(k5_yellow_1(u1_struct_0(B),C)) ) ) ).
fof(cc5_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ! [C] :
( m3_yellow_6(C,A,B)
=> ( v1_yellow_1(C)
& v4_waybel_3(C) ) ) ) ).
fof(rc9_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ? [C] :
( m3_yellow_6(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v2_pralg_1(C)
& v1_yellow_1(C)
& v4_waybel_3(C) ) ) ).
fof(fc20_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v3_struct_0(k10_yellow_6(A,B)) ) ).
fof(fc21_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k10_yellow_6(A,B))
& v3_orders_2(k10_yellow_6(A,B))
& v7_waybel_0(k10_yellow_6(A,B)) ) ) ).
fof(fc22_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> v1_realset1(k11_yellow_6(A,B)) ) ).
fof(cc6_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v3_yellow_6(B,A) ) ) ) ) ).
fof(rc10_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( l1_waybel_0(B,A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v6_waybel_0(B,A)
& v7_waybel_0(B)
& v3_yellow_6(B,A) ) ) ).
fof(cc7_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> v1_relat_1(B) ) ) ).
fof(fc23_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_relat_1(k13_yellow_6(A))
& v4_yellow_6(k13_yellow_6(A),A)
& v5_yellow_6(k13_yellow_6(A),A)
& v6_yellow_6(k13_yellow_6(A),A)
& v7_yellow_6(k13_yellow_6(A),A) ) ) ).
fof(fc24_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m4_yellow_6(B,A) )
=> ( ~ v3_struct_0(k14_yellow_6(A,B))
& v1_pre_topc(k14_yellow_6(A,B)) ) ) ).
fof(fc25_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m4_yellow_6(B,A) )
=> ( ~ v3_struct_0(k14_yellow_6(A,B))
& v1_pre_topc(k14_yellow_6(A,B))
& v2_pre_topc(k14_yellow_6(A,B)) ) ) ).
fof(rc11_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m4_yellow_6(B,A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v8_yellow_6(B,A) ) ) ).
fof(cc8_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v8_yellow_6(B,A)
=> ( v1_relat_1(B)
& v4_yellow_6(B,A)
& v5_yellow_6(B,A)
& v6_yellow_6(B,A)
& v7_yellow_6(B,A) ) ) ) ) ).
fof(cc9_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( ( v4_yellow_6(B,A)
& v5_yellow_6(B,A)
& v6_yellow_6(B,A)
& v7_yellow_6(B,A) )
=> ( v1_relat_1(B)
& v8_yellow_6(B,A) ) ) ) ) ).
fof(d1_yellow_6,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v5_seqm_3(A)
=> ( v1_xboole_0(A)
| ! [B] :
( B = k1_yellow_6(A)
<=> ? [C] :
( r2_hidden(C,k1_relat_1(A))
& B = k1_funct_1(A,C) ) ) ) ) ) ).
fof(t1_yellow_6,axiom,
$true ).
fof(t2_yellow_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] : k1_yellow_6(k2_pre_circ(A,B)) = B ) ).
fof(d2_yellow_6,axiom,
$true ).
fof(d3_yellow_6,axiom,
! [A] : k2_yellow_6(A) = k1_classes1(k5_classes1(A)) ).
fof(t3_yellow_6,axiom,
$true ).
fof(t4_yellow_6,axiom,
$true ).
fof(t5_yellow_6,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( r2_hidden(k1_relat_1(B),A)
& r1_tarski(k2_relat_1(B),A) )
=> r2_hidden(k4_card_3(B),A) ) ) ) ).
fof(t6_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ! [D] :
( m1_connsp_2(D,A,C)
=> ~ r1_xboole_0(D,B) ) ) ) ) ) ).
fof(t7_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> m2_connsp_2(k2_pre_topc(A),A,B) ) ) ).
fof(t8_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m2_connsp_2(C,A,B)
=> r1_tarski(B,C) ) ) ) ).
fof(t9_yellow_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v2_pralg_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> k1_funct_1(k12_pralg_1(A,B),C) = u1_struct_0(k10_pralg_1(A,B,C)) ) ) ) ).
fof(d4_yellow_6,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A) )
=> ( v4_waybel_3(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> ( ~ v3_struct_0(B)
& l1_struct_0(B) ) ) ) ) ).
fof(t10_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ r2_hidden(C,B)
<=> r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) ) ) ) ) ).
fof(d5_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v7_waybel_0(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,D)
& r1_orders_2(A,C,D) ) ) ) ) ) ).
fof(t11_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> k2_pre_topc(k3_yellow_3(A,B)) = k6_yellow_3(A,B,k2_pre_topc(A),k2_pre_topc(B)) ) ) ).
fof(t12_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> u1_struct_0(A) = u1_struct_0(k7_lattice3(A)) ) ).
fof(d6_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ( v1_yellow_6(B,A)
<=> v5_seqm_3(u1_waybel_0(A,B)) ) ) ) ).
fof(d7_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( ( v6_waybel_0(D,B)
& l1_waybel_0(D,B) )
=> ( D = k4_yellow_6(A,B,C)
<=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A))
& u1_waybel_0(B,D) = k2_pre_circ(u1_struct_0(D),C) ) ) ) ) ) ) ).
fof(t13_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> u1_struct_0(k4_yellow_6(A,B,C)) = u1_struct_0(A) ) ) ) ).
fof(t14_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k4_yellow_6(A,B,C)))
=> k3_waybel_0(B,k4_yellow_6(A,B,C),D) = C ) ) ) ) ).
fof(t15_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> ( v4_yellow_0(A,A)
& m1_yellow_0(A,A) ) ) ).
fof(t16_yellow_6,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> ! [C] :
( m1_yellow_0(C,B)
=> m1_yellow_0(C,A) ) ) ) ).
fof(d8_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C] :
( l1_waybel_0(C,A)
=> ( m1_yellow_6(C,A,B)
<=> ( m1_yellow_0(C,B)
& u1_waybel_0(A,C) = k8_relset_1(u1_struct_0(B),u1_struct_0(A),u1_waybel_0(A,B),u1_struct_0(C)) ) ) ) ) ) ).
fof(t17_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> m1_yellow_6(B,A,B) ) ) ).
fof(t18_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C] :
( m1_yellow_6(C,A,B)
=> ! [D] :
( m1_yellow_6(D,A,C)
=> m1_yellow_6(D,A,B) ) ) ) ) ).
fof(d9_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C] :
( m1_yellow_6(C,A,B)
=> ( v2_yellow_6(C,A,B)
<=> ( v4_yellow_0(C,B)
& m1_yellow_0(C,B) ) ) ) ) ) ).
fof(t19_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C] :
( m1_yellow_6(C,A,B)
=> r1_tarski(u1_struct_0(C),u1_struct_0(B)) ) ) ) ).
fof(t20_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C] :
( m1_yellow_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( ( D = F
& E = G
& r1_orders_2(C,F,G) )
=> r1_orders_2(B,D,E) ) ) ) ) ) ) ) ) ).
fof(t21_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_yellow_6(C,A,B)
& m1_yellow_6(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( ( D = F
& E = G
& r1_orders_2(B,D,E) )
=> r1_orders_2(C,F,G) ) ) ) ) ) ) ) ) ).
fof(d10_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( l1_waybel_0(B,A)
=> ( v1_yellow_6(B,A)
=> ( v3_struct_0(B)
| k5_yellow_6(A,B) = k1_yellow_6(u1_waybel_0(A,B)) ) ) ) ) ).
fof(t22_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k5_yellow_6(B,k4_yellow_6(A,B,C)) = C ) ) ) ).
fof(d11_yellow_6,axiom,
$true ).
fof(d12_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ( m2_yellow_6(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B))
& u1_waybel_0(A,C) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,u1_waybel_0(A,B))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(C))
& ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( r1_orders_2(C,F,G)
=> r1_orders_2(B,E,k3_yellow_6(u1_struct_0(C),B,D,G)) ) ) ) ) ) ) ) ) ) ).
fof(t23_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> m2_yellow_6(B,A,B) ) ) ).
fof(t24_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( ( m2_yellow_6(B,A,C)
& m2_yellow_6(C,A,D) )
=> m2_yellow_6(B,A,D) ) ) ) ) ) ).
fof(t25_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_waybel_0(A,B,C) = k5_yellow_6(A,B) ) ) ) ).
fof(t26_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C,D] :
~ ( r1_waybel_0(A,B,C)
& r1_waybel_0(A,B,D)
& r1_xboole_0(C,D) ) ) ) ).
fof(t27_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> ! [D] :
( r2_waybel_0(A,C,D)
=> r2_waybel_0(A,B,D) ) ) ) ) ).
fof(t28_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r1_waybel_0(A,B,C)
=> r2_waybel_0(A,B,C) ) ) ) ).
fof(t29_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> r1_waybel_0(A,B,u1_struct_0(A)) ) ) ).
fof(d13_yellow_6,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_waybel_0(B,A)
=> ! [C,D] :
( ( v6_waybel_0(D,A)
& m1_yellow_6(D,A,B) )
=> ( D = k6_yellow_6(A,B,C)
<=> ( v4_yellow_0(D,B)
& m1_yellow_0(D,B)
& u1_struct_0(D) = k5_pre_topc(B,A,u1_waybel_0(A,B),C) ) ) ) ) ) ).
fof(t30_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r2_waybel_0(A,B,C)
=> ( ~ v3_struct_0(k6_yellow_6(A,B,C))
& v7_waybel_0(k6_yellow_6(A,B,C)) ) ) ) ) ).
fof(t31_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( r2_waybel_0(A,B,C)
=> m2_yellow_6(k6_yellow_6(A,B,C),A,B) ) ) ) ).
fof(t32_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C,D] :
( m2_yellow_6(D,A,B)
=> ( D = k6_yellow_6(A,B,C)
=> r1_waybel_0(A,D,C) ) ) ) ) ).
fof(d14_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( B = k7_yellow_6(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( ~ v3_struct_0(D)
& v3_orders_2(D)
& v6_waybel_0(D,A)
& v7_waybel_0(D)
& l1_waybel_0(D,A)
& D = C
& r2_hidden(u1_struct_0(D),k2_yellow_6(u1_struct_0(A))) ) ) ) ) ).
fof(d15_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ! [C] :
( m1_pboole(C,A)
=> ( m3_yellow_6(C,A,B)
<=> ! [D] :
( r2_hidden(D,k2_relat_1(C))
=> ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,B) ) ) ) ) ) ).
fof(t33_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ! [C] :
( m1_pboole(C,A)
=> ( m3_yellow_6(C,A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> ( ~ v3_struct_0(k1_funct_1(C,D))
& v3_orders_2(k1_funct_1(C,D))
& v7_waybel_0(k1_funct_1(C,D))
& l1_waybel_0(k1_funct_1(C,D),B) ) ) ) ) ) ).
fof(d16_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v6_waybel_0(D,A)
& v7_waybel_0(D)
& l1_waybel_0(D,A) )
=> ( D = k9_yellow_6(A,B,C)
<=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = k3_yellow_3(B,k5_yellow_1(u1_struct_0(B),C))
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( ( r2_hidden(E,u1_struct_0(B))
& r2_hidden(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) )
=> k1_binop_1(u1_waybel_0(A,D),E,F) = k1_funct_1(u1_waybel_0(A,k8_yellow_6(u1_struct_0(B),A,C,E)),k1_funct_1(F,E)) ) ) ) ) ) ) ) ) ) ).
fof(t34_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> ( ( r2_hidden(B,k7_yellow_6(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r2_hidden(k8_yellow_6(u1_struct_0(B),A,C,D),k7_yellow_6(A)) ) )
=> r2_hidden(k9_yellow_6(A,B,C),k7_yellow_6(A)) ) ) ) ) ).
fof(t35_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> u1_struct_0(k9_yellow_6(A,B,C)) = k2_zfmisc_1(u1_struct_0(B),k4_card_3(k12_pralg_1(u1_struct_0(B),C))) ) ) ) ).
fof(t36_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_yellow_1(u1_struct_0(B),C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k9_yellow_6(A,B,C)))
=> ( F = k7_yellow_3(B,k5_yellow_1(u1_struct_0(B),C),D,E)
=> k3_waybel_0(A,k9_yellow_6(A,B,C),F) = k1_waybel_0(k3_waybel_3(u1_struct_0(B),C,D),A,u1_waybel_0(A,k8_yellow_6(u1_struct_0(B),A,C,D)),k4_waybel_3(u1_struct_0(B),C,E,D)) ) ) ) ) ) ) ) ).
fof(t38_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k10_yellow_6(A,B)))
=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& D = C
& r2_hidden(B,D)
& v3_pre_topc(D,A) ) ) ) ) ).
fof(t39_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,u1_struct_0(k10_yellow_6(A,B)))
<=> ( r2_hidden(B,C)
& v3_pre_topc(C,A) ) ) ) ) ) ).
fof(t40_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k10_yellow_6(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k10_yellow_6(A,B)))
=> ( r1_orders_2(k10_yellow_6(A,B),C,D)
<=> r1_tarski(D,C) ) ) ) ) ) ).
fof(d18_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k11_yellow_6(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> ! [E] :
( m1_connsp_2(E,A,D)
=> r1_waybel_0(A,B,E) ) ) ) ) ) ) ) ).
fof(t41_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> r1_tarski(k11_yellow_6(A,B),k11_yellow_6(A,C)) ) ) ) ).
fof(t42_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> r2_hidden(k5_yellow_6(A,B),k11_yellow_6(A,B)) ) ) ).
fof(t44_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_compts_1(A)
<=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,k11_yellow_6(A,B))
& r2_hidden(D,k11_yellow_6(A,B)) )
=> C = D ) ) ) ) ) ) ).
fof(d19_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( v3_yellow_6(B,A)
<=> k11_yellow_6(A,B) != k1_xboole_0 ) ) ) ).
fof(d20_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v3_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k12_yellow_6(A,B)
<=> r2_hidden(C,k11_yellow_6(A,B)) ) ) ) ) ).
fof(t45_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v1_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> k12_yellow_6(A,B) = k5_yellow_6(A,B) ) ) ).
fof(t46_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ~ r2_hidden(C,k11_yellow_6(A,B))
& ! [D] :
( m2_yellow_6(D,A,B)
=> ? [E] :
( m2_yellow_6(E,A,D)
& r2_hidden(C,k11_yellow_6(A,E)) ) ) ) ) ) ) ).
fof(t47_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ( r2_hidden(B,k7_yellow_6(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ~ r2_hidden(C,k11_yellow_6(A,B))
& ! [D] :
( m2_yellow_6(D,A,B)
=> ~ ( r2_hidden(D,k7_yellow_6(A))
& ! [E] :
( m2_yellow_6(E,A,D)
=> ~ r2_hidden(C,k11_yellow_6(A,E)) ) ) ) ) ) ) ) ) ).
fof(t48_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k11_yellow_6(A,B))
=> ! [D] :
( m3_yellow_6(D,u1_struct_0(B),A)
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r2_hidden(k3_waybel_0(A,B,E),k11_yellow_6(A,k8_yellow_6(u1_struct_0(B),A,D,E))) )
=> r2_hidden(C,k11_yellow_6(A,k9_yellow_6(A,B,D))) ) ) ) ) ) ) ).
fof(d21_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
<=> r1_tarski(B,k2_zfmisc_1(k7_yellow_6(A),u1_struct_0(A))) ) ) ).
fof(d22_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( B = k13_yellow_6(A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ( r2_hidden(C,k7_yellow_6(A))
& r2_hidden(D,k11_yellow_6(A,C)) ) ) ) ) ) ) ) ).
fof(d23_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v4_yellow_6(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v1_yellow_6(C,A)
& l1_waybel_0(C,A) )
=> ( r2_hidden(C,k7_yellow_6(A))
=> r2_hidden(k4_tarski(C,k5_yellow_6(A,C)),B) ) ) ) ) ) ).
fof(d24_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v5_yellow_6(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m2_yellow_6(D,A,C)
=> ( r2_hidden(D,k7_yellow_6(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,E),B)
=> r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ) ) ).
fof(d25_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v6_yellow_6(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(C,k7_yellow_6(A))
& ~ r2_hidden(k4_tarski(C,D),B)
& ! [E] :
( m2_yellow_6(E,A,C)
=> ~ ( r2_hidden(E,k7_yellow_6(A))
& ! [F] :
( m2_yellow_6(F,A,E)
=> ~ r2_hidden(k4_tarski(F,D),B) ) ) ) ) ) ) ) ) ) ).
fof(d26_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v7_yellow_6(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
=> ! [E] :
( m3_yellow_6(E,u1_struct_0(C),A)
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> r2_hidden(k4_tarski(k8_yellow_6(u1_struct_0(C),A,E,F),k3_waybel_0(A,C,F)),B) )
=> r2_hidden(k4_tarski(k9_yellow_6(A,C,E),D),B) ) ) ) ) ) ) ) ) ).
fof(t49_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> r1_tarski(B,k13_yellow_6(k14_yellow_6(A,B))) ) ) ).
fof(d28_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( v8_yellow_6(B,A)
<=> ( v4_yellow_6(B,A)
& v5_yellow_6(B,A)
& v6_yellow_6(B,A)
& v7_yellow_6(B,A) ) ) ) ) ).
fof(t50_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v8_yellow_6(B,A)
& m4_yellow_6(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_yellow_6(A,B))))
=> ( v3_pre_topc(C,k14_yellow_6(A,B))
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_orders_2(E)
& v7_waybel_0(E)
& l1_waybel_0(E,A) )
=> ( r2_hidden(k4_tarski(E,D),B)
=> r1_waybel_0(A,E,C) ) ) ) ) ) ) ) ) ).
fof(t51_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v8_yellow_6(B,A)
& m4_yellow_6(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_yellow_6(A,B))))
=> ( v4_pre_topc(C,k14_yellow_6(A,B))
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_orders_2(E)
& v7_waybel_0(E)
& l1_waybel_0(E,A) )
=> ( ( r2_hidden(k4_tarski(E,D),B)
& r2_waybel_0(A,E,C) )
=> r2_hidden(D,C) ) ) ) ) ) ) ) ).
fof(t52_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v8_yellow_6(B,A)
& m4_yellow_6(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_yellow_6(A,B))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_yellow_6(A,B)))
=> ~ ( r2_hidden(D,k6_pre_topc(k14_yellow_6(A,B),C))
& ! [E] :
( ( ~ v3_struct_0(E)
& v3_orders_2(E)
& v7_waybel_0(E)
& l1_waybel_0(E,k14_yellow_6(A,B)) )
=> ~ ( r2_hidden(k4_tarski(E,D),B)
& r1_tarski(k2_relat_1(u1_waybel_0(k14_yellow_6(A,B),E)),C)
& r2_hidden(D,k11_yellow_6(k14_yellow_6(A,B),E)) ) ) ) ) ) ) ) ).
fof(t53_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ( k13_yellow_6(k14_yellow_6(A,B)) = B
<=> v8_yellow_6(B,A) ) ) ) ).
fof(dt_m1_yellow_6,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_yellow_6(C,A,B)
=> l1_waybel_0(C,A) ) ) ).
fof(existence_m1_yellow_6,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ? [C] : m1_yellow_6(C,A,B) ) ).
fof(dt_m2_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m2_yellow_6(C,A,B)
=> ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,A) ) ) ) ).
fof(existence_m2_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ? [C] : m2_yellow_6(C,A,B) ) ).
fof(dt_m3_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ! [C] :
( m3_yellow_6(C,A,B)
=> m1_pboole(C,A) ) ) ).
fof(existence_m3_yellow_6,axiom,
! [A,B] :
( l1_struct_0(B)
=> ? [C] : m3_yellow_6(C,A,B) ) ).
fof(dt_m4_yellow_6,axiom,
$true ).
fof(existence_m4_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] : m4_yellow_6(B,A) ) ).
fof(dt_k1_yellow_6,axiom,
$true ).
fof(dt_k2_yellow_6,axiom,
$true ).
fof(dt_k3_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B))
& m1_subset_1(D,A) )
=> m1_subset_1(k3_yellow_6(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k3_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B))
& m1_subset_1(D,A) )
=> k3_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k4_yellow_6,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v6_waybel_0(k4_yellow_6(A,B,C),B)
& l1_waybel_0(k4_yellow_6(A,B,C),B) ) ) ).
fof(dt_k5_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& l1_waybel_0(B,A) )
=> m1_subset_1(k5_yellow_6(A,B),u1_struct_0(A)) ) ).
fof(dt_k6_yellow_6,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_waybel_0(B,A) )
=> ( v6_waybel_0(k6_yellow_6(A,B,C),A)
& m1_yellow_6(k6_yellow_6(A,B,C),A,B) ) ) ).
fof(dt_k7_yellow_6,axiom,
$true ).
fof(dt_k8_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& l1_struct_0(B)
& m3_yellow_6(C,A,B)
& m1_subset_1(D,A) )
=> ( ~ v3_struct_0(k8_yellow_6(A,B,C,D))
& v3_orders_2(k8_yellow_6(A,B,C,D))
& v7_waybel_0(k8_yellow_6(A,B,C,D))
& l1_waybel_0(k8_yellow_6(A,B,C,D),B) ) ) ).
fof(redefinition_k8_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& l1_struct_0(B)
& m3_yellow_6(C,A,B)
& m1_subset_1(D,A) )
=> k8_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k9_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A)
& m3_yellow_6(C,u1_struct_0(B),A) )
=> ( ~ v3_struct_0(k9_yellow_6(A,B,C))
& v3_orders_2(k9_yellow_6(A,B,C))
& v6_waybel_0(k9_yellow_6(A,B,C),A)
& v7_waybel_0(k9_yellow_6(A,B,C))
& l1_waybel_0(k9_yellow_6(A,B,C),A) ) ) ).
fof(dt_k10_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> l1_orders_2(k10_yellow_6(A,B)) ) ).
fof(dt_k11_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> m1_subset_1(k11_yellow_6(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k12_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v3_yellow_6(B,A)
& l1_waybel_0(B,A) )
=> m1_subset_1(k12_yellow_6(A,B),u1_struct_0(A)) ) ).
fof(dt_k13_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> m4_yellow_6(k13_yellow_6(A),A) ) ).
fof(dt_k14_yellow_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m4_yellow_6(B,A) )
=> ( v1_pre_topc(k14_yellow_6(A,B))
& l1_pre_topc(k14_yellow_6(A,B)) ) ) ).
fof(t37_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m3_yellow_6(C,u1_struct_0(B),A)
=> r1_tarski(k2_relat_1(u1_waybel_0(A,k9_yellow_6(A,B,C))),k3_tarski(a_3_0_yellow_6(A,B,C))) ) ) ) ).
fof(d17_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k10_yellow_6(A,B) = k7_lattice3(k2_yellow_1(a_2_0_yellow_6(A,B))) ) ) ).
fof(t43_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& l1_waybel_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k11_yellow_6(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
& E = a_3_1_yellow_6(A,B,D)
& r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ).
fof(d27_yellow_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m4_yellow_6(B,A)
=> ! [C] :
( ( v1_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = k14_yellow_6(A,B)
<=> ( u1_struct_0(C) = u1_struct_0(A)
& u1_pre_topc(C) = a_2_1_yellow_6(A,B) ) ) ) ) ) ).
fof(fraenkel_a_3_0_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m3_yellow_6(D,u1_struct_0(C),B) )
=> ( r2_hidden(A,a_3_0_yellow_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k2_relat_1(u1_waybel_0(B,k8_yellow_6(u1_struct_0(C),B,D,E))) ) ) ) ).
fof(fraenkel_a_2_0_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_yellow_6(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& r2_hidden(C,D)
& v3_pre_topc(D,B) ) ) ) ).
fof(fraenkel_a_3_1_yellow_6,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,B)
& m1_subset_1(D,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_1_yellow_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = k3_waybel_0(B,C,E)
& r1_orders_2(C,D,E) ) ) ) ).
fof(fraenkel_a_2_1_yellow_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& m4_yellow_6(C,B) )
=> ( r2_hidden(A,a_2_1_yellow_6(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,D)
=> ! [F] :
( ( ~ v3_struct_0(F)
& v3_orders_2(F)
& v7_waybel_0(F)
& l1_waybel_0(F,B) )
=> ( r2_hidden(k4_tarski(F,E),C)
=> r1_waybel_0(B,F,D) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------