TPTP Problem File: TOP043+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : TOP043+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Topology
% Problem : The Tichonov Theorem T24
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Sko01] Skorulski (2001), The Tichonov Theorem
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t24_yellow17 [Urb08]
% Status : Theorem
% Rating : 1.00 v3.7.0, 0.95 v3.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 102 ( 26 unt; 0 def)
% Number of atoms : 354 ( 18 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 308 ( 56 ~; 1 |; 153 &)
% ( 9 <=>; 89 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-4 aty)
% Number of variables : 197 ( 169 !; 28 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t24_yellow17,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> v2_compts_1(k4_waybel18(A,B,C)) )
=> v2_compts_1(k3_waybel18(A,B)) ) ) ) ).
fof(abstractness_v1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_pre_topc(A)
=> A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc1_finset_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_finset_1(A) ) ).
fof(cc1_monoid_0,axiom,
! [A] :
( ( v1_monoid_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_waybel18,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_waybel18(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A) ) ) ).
fof(cc2_finset_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_finset_1(B) ) ) ).
fof(d13_funct_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( C = k10_relat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,k1_relat_1(A))
& r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ).
fof(d3_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_pre_topc(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = k3_waybel18(A,B)
<=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
& m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = k3_tarski(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( r2_hidden(C,D)
& r2_hidden(D,A) ) ) ) ).
fof(dt_g1_pre_topc,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( v1_pre_topc(g1_pre_topc(A,B))
& l1_pre_topc(g1_pre_topc(A,B)) ) ) ).
fof(dt_k10_relat_1,axiom,
$true ).
fof(dt_k12_pralg_1,axiom,
! [A,B] :
( ( v2_pralg_1(B)
& m1_pboole(B,A) )
=> m1_pboole(k12_pralg_1(A,B),A) ) ).
fof(dt_k1_funct_1,axiom,
$true ).
fof(dt_k1_relat_1,axiom,
$true ).
fof(dt_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_waybel18,axiom,
! [A,B] :
( ( v1_waybel18(B)
& m1_pboole(B,A) )
=> m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_tarski,axiom,
$true ).
fof(dt_k3_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B))
& l1_pre_topc(k3_waybel18(A,B)) ) ) ).
fof(dt_k4_card_3,axiom,
$true ).
fof(dt_k4_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( ~ v3_struct_0(k4_waybel18(A,B,C))
& l1_pre_topc(k4_waybel18(A,B,C)) ) ) ).
fof(dt_k5_pre_topc,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_waybel18,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
& m1_subset_1(D,A) )
=> m1_subset_1(k5_waybel18(A,B,C,D),u1_struct_0(k4_waybel18(A,B,D))) ) ).
fof(dt_k6_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k6_waybel18(A,B,C))
& v1_funct_2(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C)))
& m2_relset_1(k6_waybel18(A,B,C),u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C))) ) ) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_m1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m2_cantor_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m2_cantor_1(B,A)
=> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_u1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(existence_l1_pre_topc,axiom,
? [A] : l1_pre_topc(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_m1_pboole,axiom,
! [A] :
? [B] : m1_pboole(B,A) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m2_cantor_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m2_cantor_1(B,A) ) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& v1_finset_1(B) )
=> v1_finset_1(k2_zfmisc_1(A,B)) ) ).
fof(fc1_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(k1_tarski(A))
& v1_finset_1(k1_tarski(A)) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ).
fof(fc1_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k3_waybel18(A,B))
& v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B)) ) ) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0) ).
fof(fc2_cantor_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ v1_xboole_0(u1_pre_topc(A)) ) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(k2_pre_topc(A)) ) ).
fof(fc2_subset_1,axiom,
! [A] : ~ v1_xboole_0(k1_tarski(A)) ).
fof(fc2_waybel18,axiom,
! [A,B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k3_waybel18(A,B))
& v1_pre_topc(k3_waybel18(A,B))
& v2_pre_topc(k3_waybel18(A,B))
& v1_monoid_0(k3_waybel18(A,B)) ) ) ).
fof(fc3_card_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> v1_fraenkel(k4_card_3(A)) ) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ).
fof(fc5_card_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ( ~ v1_xboole_0(k4_card_3(A))
& v1_fraenkel(k4_card_3(A)) ) ) ).
fof(fc5_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_pre_topc(k2_pre_topc(A),A) ) ).
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(free_g1_pre_topc,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C,D] :
( g1_pre_topc(A,B) = g1_pre_topc(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(rc1_finset_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A) ) ).
fof(rc1_monoid_0,axiom,
? [A] :
( l1_struct_0(A)
& v1_monoid_0(A) ) ).
fof(rc1_pre_topc,axiom,
? [A] :
( l1_pre_topc(A)
& v1_pre_topc(A) ) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B) ) ) ).
fof(rc1_waybel18,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_waybel18(B) ) ).
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A) ).
fof(rc2_pre_topc,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A) ) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& v1_xboole_0(B) ) ).
fof(rc2_waybel18,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v4_waybel_3(B)
& v2_pralg_1(B)
& v1_waybel18(B) ) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ v1_xboole_0(A) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
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(rc4_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc6_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v4_pre_topc(B,A) ) ) ).
fof(rc7_pre_topc,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)))
& ~ v1_xboole_0(B)
& v4_pre_topc(B,A) ) ) ).
fof(redefinition_k1_struct_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k1_struct_0(A,B) = k1_tarski(B) ) ).
fof(redefinition_k4_waybel18,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k4_waybel18(A,B,C) = k1_funct_1(B,C) ) ).
fof(redefinition_k5_pre_topc,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D) ) ).
fof(redefinition_k5_waybel18,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
& m1_subset_1(D,A) )
=> k5_waybel18(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(s1_yellow17__e8_25__yellow17,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A)
& m2_cantor_1(C,k3_waybel18(A,B))
& m1_subset_1(D,k1_zfmisc_1(C)) )
=> ( ! [E] :
( m1_subset_1(E,A)
=> ? [F] :
( m1_subset_1(F,u1_struct_0(k4_waybel18(A,B,E)))
& ! [G] :
( ( v1_finset_1(G)
& m1_subset_1(G,k1_zfmisc_1(D)) )
=> ~ r1_tarski(k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,E),k6_waybel18(A,B,E),k1_tarski(F)),k3_tarski(G)) ) ) )
=> ? [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel18(A,B)))
& ! [F] :
( m1_subset_1(F,A)
=> ! [H] :
( ( v1_finset_1(H)
& m1_subset_1(H,k1_zfmisc_1(D)) )
=> ~ r1_tarski(k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,F),k6_waybel18(A,B,F),k1_tarski(k5_waybel18(A,B,E,F))),k3_tarski(H)) ) ) ) ) ) ).
fof(t12_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> k2_pre_topc(A) = u1_struct_0(A) ) ).
fof(t16_yellow17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_cantor_1(B,A)
=> ( v2_compts_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(B))
=> ~ ( r1_tarski(k2_pre_topc(A),k3_tarski(C))
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(C)) )
=> ~ r1_tarski(k2_pre_topc(A),k3_tarski(D)) ) ) ) ) ) ) ).
fof(t178_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) ) ) ).
fof(t17_yellow17,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
~ ( r2_hidden(C,k2_waybel18(A,B))
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,D))))
=> ~ ( v3_pre_topc(E,k4_waybel18(A,B,D))
& k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,D),k6_waybel18(A,B,D),E) = C ) ) ) ) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t23_yellow17,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k2_waybel18(A,B)))
=> ~ ( ! [E] :
( m1_subset_1(E,A)
=> v2_compts_1(k4_waybel18(A,B,E)) )
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(D)) )
=> ~ r1_tarski(k2_pre_topc(k3_waybel18(A,B)),k3_tarski(E)) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C)))
=> ? [F] :
( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(D))
& r1_tarski(k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),k1_struct_0(k4_waybel18(A,B,C),E)),k3_tarski(F)) ) ) ) ) ) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t31_zfmisc_1,axiom,
! [A] : k3_tarski(k1_tarski(A)) = A ).
fof(t37_zfmisc_1,axiom,
! [A,B] :
( r1_tarski(k1_tarski(A),B)
<=> r2_hidden(A,B) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
fof(t8_yellow17,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_waybel18(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel18(A,B)))
=> k1_funct_1(k6_waybel18(A,B,C),D) = k5_waybel18(A,B,D,C) ) ) ) ) ).
%------------------------------------------------------------------------------