TPTP Problem File: TOP043+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : TOP043+3 : 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 v3.4.0
% Syntax : Number of formulae : 18468 (2899 unt; 0 def)
% Number of atoms : 129687 (12435 equ)
% Maximal formula atoms : 70 ( 7 avg)
% Number of connectives : 127517 (16298 ~; 587 |;66527 &)
% (3519 <=>;40586 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 1167 (1165 usr; 2 prp; 0-6 aty)
% Number of functors : 2726 (2726 usr; 659 con; 0-10 aty)
% Number of variables : 48214 (45755 !;2459 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Chainy small version: includes all preceding MML articles that
% are included in any Bushy version.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
include('Axioms/SET007/SET007+0.ax').
include('Axioms/SET007/SET007+1.ax').
include('Axioms/SET007/SET007+2.ax').
include('Axioms/SET007/SET007+3.ax').
include('Axioms/SET007/SET007+4.ax').
include('Axioms/SET007/SET007+5.ax').
include('Axioms/SET007/SET007+6.ax').
include('Axioms/SET007/SET007+7.ax').
include('Axioms/SET007/SET007+8.ax').
include('Axioms/SET007/SET007+9.ax').
include('Axioms/SET007/SET007+10.ax').
include('Axioms/SET007/SET007+11.ax').
include('Axioms/SET007/SET007+13.ax').
include('Axioms/SET007/SET007+14.ax').
include('Axioms/SET007/SET007+15.ax').
include('Axioms/SET007/SET007+16.ax').
include('Axioms/SET007/SET007+17.ax').
include('Axioms/SET007/SET007+18.ax').
include('Axioms/SET007/SET007+19.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+21.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+23.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+25.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+32.ax').
include('Axioms/SET007/SET007+33.ax').
include('Axioms/SET007/SET007+34.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.ax').
include('Axioms/SET007/SET007+50.ax').
include('Axioms/SET007/SET007+51.ax').
include('Axioms/SET007/SET007+54.ax').
include('Axioms/SET007/SET007+55.ax').
include('Axioms/SET007/SET007+59.ax').
include('Axioms/SET007/SET007+60.ax').
include('Axioms/SET007/SET007+61.ax').
include('Axioms/SET007/SET007+64.ax').
include('Axioms/SET007/SET007+66.ax').
include('Axioms/SET007/SET007+67.ax').
include('Axioms/SET007/SET007+68.ax').
include('Axioms/SET007/SET007+71.ax').
include('Axioms/SET007/SET007+75.ax').
include('Axioms/SET007/SET007+76.ax').
include('Axioms/SET007/SET007+77.ax').
include('Axioms/SET007/SET007+79.ax').
include('Axioms/SET007/SET007+80.ax').
include('Axioms/SET007/SET007+86.ax').
include('Axioms/SET007/SET007+91.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+125.ax').
include('Axioms/SET007/SET007+126.ax').
include('Axioms/SET007/SET007+148.ax').
include('Axioms/SET007/SET007+159.ax').
include('Axioms/SET007/SET007+165.ax').
include('Axioms/SET007/SET007+170.ax').
include('Axioms/SET007/SET007+182.ax').
include('Axioms/SET007/SET007+186.ax').
include('Axioms/SET007/SET007+188.ax').
include('Axioms/SET007/SET007+190.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+202.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+207.ax').
include('Axioms/SET007/SET007+209.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+211.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+217.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+223.ax').
include('Axioms/SET007/SET007+224.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+227.ax').
include('Axioms/SET007/SET007+237.ax').
include('Axioms/SET007/SET007+241.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+246.ax').
include('Axioms/SET007/SET007+247.ax').
include('Axioms/SET007/SET007+248.ax').
include('Axioms/SET007/SET007+252.ax').
include('Axioms/SET007/SET007+253.ax').
include('Axioms/SET007/SET007+255.ax').
include('Axioms/SET007/SET007+256.ax').
include('Axioms/SET007/SET007+276.ax').
include('Axioms/SET007/SET007+278.ax').
include('Axioms/SET007/SET007+279.ax').
include('Axioms/SET007/SET007+280.ax').
include('Axioms/SET007/SET007+281.ax').
include('Axioms/SET007/SET007+293.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+297.ax').
include('Axioms/SET007/SET007+298.ax').
include('Axioms/SET007/SET007+299.ax').
include('Axioms/SET007/SET007+301.ax').
include('Axioms/SET007/SET007+308.ax').
include('Axioms/SET007/SET007+309.ax').
include('Axioms/SET007/SET007+311.ax').
include('Axioms/SET007/SET007+312.ax').
include('Axioms/SET007/SET007+317.ax').
include('Axioms/SET007/SET007+321.ax').
include('Axioms/SET007/SET007+322.ax').
include('Axioms/SET007/SET007+327.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+338.ax').
include('Axioms/SET007/SET007+339.ax').
include('Axioms/SET007/SET007+354.ax').
include('Axioms/SET007/SET007+363.ax').
include('Axioms/SET007/SET007+365.ax').
include('Axioms/SET007/SET007+370.ax').
include('Axioms/SET007/SET007+375.ax').
include('Axioms/SET007/SET007+377.ax').
include('Axioms/SET007/SET007+384.ax').
include('Axioms/SET007/SET007+387.ax').
include('Axioms/SET007/SET007+388.ax').
include('Axioms/SET007/SET007+393.ax').
include('Axioms/SET007/SET007+394.ax').
include('Axioms/SET007/SET007+395.ax').
include('Axioms/SET007/SET007+396.ax').
include('Axioms/SET007/SET007+399.ax').
include('Axioms/SET007/SET007+401.ax').
include('Axioms/SET007/SET007+405.ax').
include('Axioms/SET007/SET007+406.ax').
include('Axioms/SET007/SET007+407.ax').
include('Axioms/SET007/SET007+411.ax').
include('Axioms/SET007/SET007+412.ax').
include('Axioms/SET007/SET007+426.ax').
include('Axioms/SET007/SET007+427.ax').
include('Axioms/SET007/SET007+432.ax').
include('Axioms/SET007/SET007+433.ax').
include('Axioms/SET007/SET007+438.ax').
include('Axioms/SET007/SET007+441.ax').
include('Axioms/SET007/SET007+445.ax').
include('Axioms/SET007/SET007+448.ax').
include('Axioms/SET007/SET007+449.ax').
include('Axioms/SET007/SET007+455.ax').
include('Axioms/SET007/SET007+463.ax').
include('Axioms/SET007/SET007+464.ax').
include('Axioms/SET007/SET007+466.ax').
include('Axioms/SET007/SET007+480.ax').
include('Axioms/SET007/SET007+481.ax').
include('Axioms/SET007/SET007+483.ax').
include('Axioms/SET007/SET007+484.ax').
include('Axioms/SET007/SET007+485.ax').
include('Axioms/SET007/SET007+486.ax').
include('Axioms/SET007/SET007+487.ax').
include('Axioms/SET007/SET007+488.ax').
include('Axioms/SET007/SET007+489.ax').
include('Axioms/SET007/SET007+490.ax').
include('Axioms/SET007/SET007+492.ax').
include('Axioms/SET007/SET007+493.ax').
include('Axioms/SET007/SET007+494.ax').
include('Axioms/SET007/SET007+495.ax').
include('Axioms/SET007/SET007+496.ax').
include('Axioms/SET007/SET007+497.ax').
include('Axioms/SET007/SET007+498.ax').
include('Axioms/SET007/SET007+500.ax').
include('Axioms/SET007/SET007+503.ax').
include('Axioms/SET007/SET007+505.ax').
include('Axioms/SET007/SET007+506.ax').
include('Axioms/SET007/SET007+509.ax').
include('Axioms/SET007/SET007+513.ax').
include('Axioms/SET007/SET007+514.ax').
include('Axioms/SET007/SET007+517.ax').
include('Axioms/SET007/SET007+520.ax').
include('Axioms/SET007/SET007+525.ax').
include('Axioms/SET007/SET007+527.ax').
include('Axioms/SET007/SET007+530.ax').
include('Axioms/SET007/SET007+537.ax').
include('Axioms/SET007/SET007+538.ax').
include('Axioms/SET007/SET007+542.ax').
include('Axioms/SET007/SET007+544.ax').
include('Axioms/SET007/SET007+545.ax').
include('Axioms/SET007/SET007+558.ax').
include('Axioms/SET007/SET007+559.ax').
include('Axioms/SET007/SET007+560.ax').
include('Axioms/SET007/SET007+561.ax').
include('Axioms/SET007/SET007+567.ax').
include('Axioms/SET007/SET007+572.ax').
include('Axioms/SET007/SET007+573.ax').
include('Axioms/SET007/SET007+586.ax').
include('Axioms/SET007/SET007+603.ax').
include('Axioms/SET007/SET007+620.ax').
include('Axioms/SET007/SET007+636.ax').
include('Axioms/SET007/SET007+637.ax').
%------------------------------------------------------------------------------
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(t1_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D] :
( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(A,B)))
=> ( ~ r1_xboole_0(k10_relat_1(k3_pralg_3(A,B),k1_tarski(C)),k10_relat_1(k3_pralg_3(A,B),D))
=> r2_hidden(C,D) ) ) ) ).
fof(t2_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( r2_hidden(D,k1_funct_1(A,C))
& r2_hidden(B,k4_card_3(A)) )
=> r2_hidden(k2_funct_7(B,C,D),k4_card_3(A)) ) ) ) ).
fof(t3_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( k4_card_3(A) = k1_xboole_0
| k2_relat_1(k3_pralg_3(A,B)) = k1_funct_1(A,B) ) ) ) ).
fof(t4_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k10_relat_1(k3_pralg_3(A,B),k1_funct_1(A,B)) = k4_card_3(A) ) ) ).
fof(t5_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( r2_hidden(D,k1_funct_1(A,C))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(B,k4_card_3(A)) )
=> r2_hidden(k2_funct_7(B,C,D),k10_relat_1(k3_pralg_3(A,C),k1_tarski(D))) ) ) ) ).
fof(l6_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D,E,F] :
( m1_subset_1(F,k1_zfmisc_1(k1_funct_1(A,D)))
=> ( ( r2_hidden(B,k4_card_3(A))
& r2_hidden(k2_funct_7(B,C,E),k10_relat_1(k3_pralg_3(A,D),F)) )
=> ( C = D
| r2_hidden(B,k10_relat_1(k3_pralg_3(A,D),F)) ) ) ) ) ) ).
fof(t6_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D,E,F] :
( m1_subset_1(F,k1_zfmisc_1(k1_funct_1(A,D)))
=> ( ( r2_hidden(E,k1_funct_1(A,C))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(B,k4_card_3(A)) )
=> ( C = D
| ( r2_hidden(B,k10_relat_1(k3_pralg_3(A,D),F))
<=> r2_hidden(k2_funct_7(B,C,E),k10_relat_1(k3_pralg_3(A,D),F)) ) ) ) ) ) ) ).
fof(t7_yellow17,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E] :
( m1_subset_1(E,k1_zfmisc_1(k1_funct_1(A,C)))
=> ( ( r2_hidden(D,k1_funct_1(A,B))
& r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A)) )
=> ( k4_card_3(A) = k1_xboole_0
| E = k1_funct_1(A,C)
| ( r1_tarski(k10_relat_1(k3_pralg_3(A,B),k1_tarski(D)),k10_relat_1(k3_pralg_3(A,C),E))
<=> ( B = C
& r2_hidden(D,E) ) ) ) ) ) ) ).
fof(s1_yellow17,axiom,
( ! [A] :
( m1_subset_1(A,f1_s1_yellow17)
=> ? [B] :
( m1_subset_1(B,u1_struct_0(k4_waybel18(f1_s1_yellow17,f2_s1_yellow17,A)))
& p1_s1_yellow17(B,A) ) )
=> ? [A] :
( m1_subset_1(A,u1_struct_0(k3_waybel18(f1_s1_yellow17,f2_s1_yellow17)))
& ! [B] :
( m1_subset_1(B,f1_s1_yellow17)
=> p1_s1_yellow17(k5_waybel18(f1_s1_yellow17,f2_s1_yellow17,A,B),B) ) ) ) ).
fof(dt_f1_s1_yellow17,axiom,
~ v1_xboole_0(f1_s1_yellow17) ).
fof(dt_f2_s1_yellow17,axiom,
( v4_waybel_3(f2_s1_yellow17)
& v1_waybel18(f2_s1_yellow17)
& m1_pboole(f2_s1_yellow17,f1_s1_yellow17) ) ).
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) ) ) ) ) ).
fof(t9_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(k4_waybel18(A,B,C)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))
=> ( ~ r1_xboole_0(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),D)),k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),E))
=> r2_hidden(D,E) ) ) ) ) ) ) ).
fof(t10_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)
=> k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),k2_pre_topc(k4_waybel18(A,B,C))) = k2_pre_topc(k3_waybel18(A,B)) ) ) ) ).
fof(t11_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(k4_waybel18(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel18(A,B)))
=> r2_hidden(k2_funct_7(E,C,D),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),D))) ) ) ) ) ) ).
fof(t12_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,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,D))))
=> ( F != k2_pre_topc(k4_waybel18(A,B,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)),k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,D),k6_waybel18(A,B,D),F))
<=> ( C = D
& r2_hidden(E,F) ) ) ) ) ) ) ) ) ) ).
fof(t13_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,A)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,D))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k3_waybel18(A,B)))
=> ( C != D
=> ( r2_hidden(G,k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,D),k6_waybel18(A,B,D),F))
<=> r2_hidden(k2_funct_7(G,C,E),k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,D),k6_waybel18(A,B,D),F)) ) ) ) ) ) ) ) ) ) ).
fof(t14_yellow17,axiom,
$true ).
fof(t15_yellow17,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ~ ( v1_tops_2(B,A)
& r1_tarski(k2_pre_topc(A),k3_tarski(B))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ~ ( r1_tarski(C,B)
& r1_tarski(k2_pre_topc(A),k3_tarski(C))
& v1_finset_1(C) ) ) ) ) ) ) ).
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(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(t18_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(k4_waybel18(A,B,C)))
=> ! [E] :
~ ( r2_hidden(E,k2_waybel18(A,B))
& 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),D)),E)
& E != k2_pre_topc(k3_waybel18(A,B))
& ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))
=> ~ ( F != k2_pre_topc(k4_waybel18(A,B,C))
& r2_hidden(D,F)
& v3_pre_topc(F,k4_waybel18(A,B,C))
& E = k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),F) ) ) ) ) ) ) ) ).
fof(t19_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] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))) )
=> ( r1_tarski(k2_pre_topc(k4_waybel18(A,B,C)),k3_tarski(D))
=> r1_tarski(k2_pre_topc(k3_waybel18(A,B)),k3_tarski(a_4_0_yellow17(A,B,C,D))) ) ) ) ) ) ).
fof(t20_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(k4_waybel18(A,B,C)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k2_waybel18(A,B)))
=> ( ( 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),D)),k3_tarski(E))
& ! [F] :
~ ( r2_hidden(F,k2_waybel18(A,B))
& r2_hidden(F,E)
& 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),D)),F) ) )
=> r1_tarski(k2_pre_topc(k3_waybel18(A,B)),k3_tarski(E)) ) ) ) ) ) ) ).
fof(t21_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] :
( ( 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))
& ! [G] :
~ ( r2_hidden(G,k2_waybel18(A,B))
& r2_hidden(G,F)
& 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)),G) ) ) ) ) ) ) ) ) ) ).
fof(t22_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] :
( ( 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))
& ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C))))
=> ~ ( G != k2_pre_topc(k4_waybel18(A,B,C))
& r2_hidden(E,G)
& r2_hidden(k5_pre_topc(k3_waybel18(A,B),k4_waybel18(A,B,C),k6_waybel18(A,B,C),G),F)
& v3_pre_topc(G,k4_waybel18(A,B,C)) ) ) ) ) ) ) ) ) ) ) ).
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(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)) ) ) ) ).
%------------------------------------------------------------------------------