SET007 Axioms: SET007+546.ax
%------------------------------------------------------------------------------
% File : SET007+546 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Characterization of Hausdorff Spaces
% 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 : yellow12 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 5 unt; 0 def)
% Number of atoms : 588 ( 63 equ)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 599 ( 76 ~; 0 |; 325 &)
% ( 6 <=>; 192 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 64 ( 63 usr; 0 prp; 1-4 aty)
% Number of functors : 50 ( 50 usr; 0 con; 1-5 aty)
% Number of variables : 207 ( 197 !; 10 ?)
% 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(fc1_yellow12,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_xboole_0(k3_tarski(A))
& v1_membered(k3_tarski(A))
& v2_membered(k3_tarski(A))
& v3_membered(k3_tarski(A))
& v4_membered(k3_tarski(A))
& v5_membered(k3_tarski(A)) ) ) ).
fof(fc2_yellow12,axiom,
! [A,B] :
( v1_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)))
& v1_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)))
& v2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) ) ).
fof(fc3_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k4_waybel_2(A))
& v1_relat_1(k4_waybel_2(A))
& v1_funct_1(k4_waybel_2(A))
& v1_funct_2(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v1_partfun1(k4_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v17_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v19_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v21_waybel_0(k4_waybel_2(A),k3_yellow_3(A,A),A)
& v5_orders_3(k4_waybel_2(A),k3_yellow_3(A,A),A) ) ) ).
fof(fc4_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k5_waybel_2(A))
& v1_relat_1(k5_waybel_2(A))
& v1_funct_1(k5_waybel_2(A))
& v1_funct_2(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v1_partfun1(k5_waybel_2(A),u1_struct_0(k3_yellow_3(A,A)),u1_struct_0(A))
& v18_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
& v20_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
& v22_waybel_0(k5_waybel_2(A),k3_yellow_3(A,A),A)
& v5_orders_3(k5_waybel_2(A),k3_yellow_3(A,A),A) ) ) ).
fof(fc5_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
& v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ).
fof(fc6_yellow12,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
& v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ).
fof(cc1_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(cc2_yellow12,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ! [C] :
( m1_yellow_8(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(rc1_yellow12,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& l1_pre_topc(B) )
=> ? [C] :
( m3_yellow_9(C,A,B)
& v1_pre_topc(C)
& v2_pre_topc(C) ) ) ).
fof(rc2_yellow12,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& l1_pre_topc(B) )
=> ? [C] :
( m3_yellow_9(C,A,B)
& ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_pre_topc(C) ) ) ).
fof(rc3_yellow12,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& l1_pre_topc(B) )
=> ? [C] :
( m3_yellow_9(C,B,A)
& ~ v3_struct_0(C)
& v1_pre_topc(C)
& v2_pre_topc(C) ) ) ).
fof(t1_yellow12,axiom,
! [A,B] : r1_tarski(k10_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),B),k2_zfmisc_1(B,B)) ).
fof(t2_yellow12,axiom,
! [A,B] : r1_tarski(k11_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),k2_zfmisc_1(B,B)),B) ).
fof(t3_yellow12,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> k11_relset_1(A,k2_zfmisc_1(A,A),k12_funct_3(A),k12_mcart_1(A,A,B,B)) = B ) ).
fof(t4_yellow12,axiom,
! [A,B] :
( k1_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k2_zfmisc_1(A,B)
& k2_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k2_zfmisc_1(B,A) ) ).
fof(t5_yellow12,axiom,
! [A,B,C,D] : r1_tarski(k9_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)),k2_zfmisc_1(C,D)),k2_zfmisc_1(D,C)) ).
fof(t6_yellow12,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> k9_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = k12_mcart_1(B,A,D,C) ) ) ).
fof(t7_yellow12,axiom,
! [A,B] : v2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) ).
fof(t8_yellow12,axiom,
! [A,B] : k2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k13_funct_3(k10_funct_3(B,A),k9_funct_3(B,A)) ).
fof(t9_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = E
& D = F )
=> k12_lattice3(A,C,D) = k11_lattice3(B,E,F) ) ) ) ) ) ) ) ).
fof(t10_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = E
& D = F )
=> k13_lattice3(A,C,D) = k10_lattice3(B,E,F) ) ) ) ) ) ) ) ).
fof(t11_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(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(B)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = E
& D = F )
=> k4_yellow_4(A,C,D) = k3_yellow_4(B,E,F) ) ) ) ) ) ) ) ).
fof(t12_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(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(B)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = E
& D = F )
=> k2_yellow_4(A,C,D) = k1_yellow_4(B,E,F) ) ) ) ) ) ) ) ).
fof(t13_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = D )
=> ( k1_waybel_3(A,C) = k1_waybel_3(B,D)
& k2_waybel_3(A,C) = k2_waybel_3(B,D) ) ) ) ) ) ) ).
fof(t14_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_waybel_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> v2_waybel_2(B) ) ) ) ).
fof(t15_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> v3_waybel_3(B) ) ) ) ).
fof(t16_yellow12,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = D )
=> k5_yellow_0(A,C) = k5_yellow_0(B,D) ) ) ) ) ) ).
fof(t17_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_yellow_0(C,A)
=> ! [D] :
( m1_yellow_0(D,B)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& v5_yellow_0(C,A) )
=> v5_yellow_0(D,B) ) ) ) ) ) ).
fof(t18_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_yellow_0(C,A)
=> ! [D] :
( m1_yellow_0(D,B)
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& v6_yellow_0(C,A) )
=> v6_yellow_0(D,B) ) ) ) ) ) ).
fof(t19_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = D
& v3_waybel11(C,A) )
=> v3_waybel11(D,B) ) ) ) ) ) ).
fof(t20_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& C = D
& v2_waybel11(C,A) )
=> v2_waybel11(D,B) ) ) ) ) ) ).
fof(t21_yellow12,axiom,
! [A] :
( ( v4_orders_2(A)
& v2_lattice3(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)))
=> ! [D] :
( ( v13_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_xboole_0(B,D)
=> r1_xboole_0(k4_yellow_4(A,B,C),D) ) ) ) ) ) ).
fof(t22_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> r1_tarski(k6_partfun1(u1_struct_0(A)),k3_xboole_0(u1_orders_2(A),u1_orders_2(k7_lattice3(A)))) ) ).
fof(t23_yellow12,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> r1_tarski(k3_xboole_0(u1_orders_2(A),u1_orders_2(k7_lattice3(A))),k6_partfun1(u1_struct_0(A))) ) ).
fof(t24_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( r2_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k4_waybel_2(A),B))
=> r3_waybel_0(k3_yellow_3(A,A),A,k4_waybel_2(A),B) ) ) ) ).
fof(t25_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( r1_yellow_0(A,k4_pre_topc(k3_yellow_3(A,A),A,k5_waybel_2(A),B))
=> r4_waybel_0(k3_yellow_3(A,A),A,k5_waybel_2(A),B) ) ) ) ).
fof(t26_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_yellow_0(k5_yellow_0(A,B),A)
=> v2_waybel_0(B,A) ) ) ) ).
fof(t27_yellow12,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_yellow_0(k5_yellow_0(A,B),A)
=> v1_waybel_0(B,A) ) ) ) ).
fof(t28_yellow12,axiom,
! [A] :
( ( v3_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)))
=> ( r2_yellow_4(A,k5_waybel_0(A,C),B)
=> r1_tarski(k5_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) ).
fof(t29_yellow12,axiom,
! [A] :
( ( v3_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_yellow_4(A,B,k4_waybel_0(A,C))
=> r1_tarski(k4_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) ).
fof(t30_yellow12,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,C)
=> r1_tarski(k7_waybel_0(A,B),k5_waybel_0(A,C)) ) ) ) ) ).
fof(t31_yellow12,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,C)
=> r1_tarski(k6_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) ).
fof(t32_yellow12,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_cantor_1(C,A)
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> m1_cantor_1(C,B) ) ) ) ) ).
fof(t33_yellow12,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m2_cantor_1(C,A)
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> m2_cantor_1(C,B) ) ) ) ) ).
fof(t34_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(t35_yellow12,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_yellow_8(C,A,B)
=> ~ v1_xboole_0(C) ) ) ) ).
fof(t36_yellow12,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D))
& E = F
& v5_pre_topc(E,A,C) )
=> v5_pre_topc(F,B,D) ) ) ) ) ) ) ) ).
fof(t38_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_funct_1(k12_funct_3(u1_struct_0(A)))
& v1_funct_2(k12_funct_3(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k6_borsuk_1(A,A)))
& v5_pre_topc(k12_funct_3(u1_struct_0(A)),A,k6_borsuk_1(A,A))
& m2_relset_1(k12_funct_3(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k6_borsuk_1(A,A))) ) ) ).
fof(t39_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v1_funct_1(k9_funct_3(u1_struct_0(A),u1_struct_0(B)))
& v1_funct_2(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A))
& v5_pre_topc(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),k6_borsuk_1(A,B),A)
& m2_relset_1(k9_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A)) ) ) ) ).
fof(t40_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v1_funct_1(k10_funct_3(u1_struct_0(A),u1_struct_0(B)))
& v1_funct_2(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B))
& v5_pre_topc(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k6_borsuk_1(A,B),B)
& m2_relset_1(k10_funct_3(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B)) ) ) ) ).
fof(t41_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v5_pre_topc(E,A,C)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( v1_funct_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
& v1_funct_2(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
& v5_pre_topc(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,k6_borsuk_1(B,C))
& m2_relset_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) ) ) ) ) ) ) ).
fof(t42_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( v1_funct_1(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))))
& v1_funct_2(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A)))
& v5_pre_topc(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),k6_borsuk_1(A,B),k6_borsuk_1(B,A))
& m2_relset_1(k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B))),u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A))) ) ) ) ).
fof(t43_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A)))
& m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(k6_borsuk_1(B,A))) )
=> ( C = k14_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),u1_struct_0(A),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),k9_funct_3(u1_struct_0(A),u1_struct_0(B)))
=> v3_tops_2(C,k6_borsuk_1(A,B),k6_borsuk_1(B,A)) ) ) ) ) ).
fof(t44_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> r1_t_0topsp(k6_borsuk_1(A,B),k6_borsuk_1(B,A)) ) ) ).
fof(t46_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_compts_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,A))))
=> ( B = k6_partfun1(u1_struct_0(A))
=> v4_pre_topc(B,k6_borsuk_1(A,A)) ) ) ) ) ).
fof(t47_yellow12,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( l1_pre_topc(C)
=> ( m3_yellow_9(A,B,C)
<=> m3_yellow_9(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),B,C) ) ) ) ) ).
fof(t49_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( m3_yellow_9(E,k6_borsuk_1(A,C),k6_borsuk_1(B,D))
=> ! [F] :
( m3_yellow_9(F,A,B)
=> ! [G] :
( m3_yellow_9(G,C,D)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_struct_0(C) = u1_struct_0(D) )
=> ( u1_struct_0(k6_borsuk_1(F,G)) = u1_struct_0(E)
& u1_pre_topc(k6_borsuk_1(F,G)) = u1_pre_topc(E) ) ) ) ) ) ) ) ) ) ).
fof(t50_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( m3_yellow_9(E,A,B)
=> ! [F] :
( m3_yellow_9(F,C,D)
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_struct_0(C) = u1_struct_0(D) )
=> m3_yellow_9(k6_borsuk_1(E,F),k6_borsuk_1(A,C),k6_borsuk_1(B,D)) ) ) ) ) ) ) ) ).
fof(t37_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> k6_partfun1(u1_struct_0(A)) = a_1_0_yellow12(A) ) ).
fof(t45_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_compts_1(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( E = a_4_0_yellow12(A,B,C,D)
=> v3_pre_topc(E,A) ) )
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( E = a_4_1_yellow12(A,B,C,D)
=> v4_pre_topc(E,A) ) ) ) ) ) ) ) ).
fof(t48_yellow12,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( m3_yellow_9(E,k6_borsuk_1(A,C),k6_borsuk_1(B,D))
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& u1_struct_0(C) = u1_struct_0(D) )
=> m1_cantor_1(a_4_2_yellow12(A,B,C,D),E) ) ) ) ) ) ) ).
fof(fraenkel_a_1_0_yellow12,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r2_hidden(A,a_1_0_yellow12(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(B,B)))
& A = C
& k1_funct_1(k9_funct_3(u1_struct_0(B),u1_struct_0(B)),C) = k1_funct_1(k10_funct_3(u1_struct_0(B),u1_struct_0(B)),C) ) ) ) ).
fof(fraenkel_a_4_0_yellow12,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& v3_compts_1(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_4_0_yellow12(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = F
& k1_waybel_0(B,C,D,F) != k1_waybel_0(B,C,E,F) ) ) ) ).
fof(fraenkel_a_4_1_yellow12,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& v3_compts_1(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_4_1_yellow12(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = F
& k1_waybel_0(B,C,D,F) = k1_waybel_0(B,C,E,F) ) ) ) ).
fof(fraenkel_a_4_2_yellow12,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C)
& ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D)
& ~ v3_struct_0(E)
& v2_pre_topc(E)
& l1_pre_topc(E) )
=> ( r2_hidden(A,a_4_2_yellow12(B,C,D,E))
<=> ? [F,G,H,I] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C)))
& m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D)))
& m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E)))
& A = k3_xboole_0(k7_borsuk_1(B,D,F,H),k7_borsuk_1(C,E,G,I))
& v3_pre_topc(F,B)
& v3_pre_topc(G,C)
& v3_pre_topc(H,D)
& v3_pre_topc(I,E) ) ) ) ).
%------------------------------------------------------------------------------