TPTP Problem File: TOP045+2.p
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%------------------------------------------------------------------------------
% File : TOP045+2 : TPTP v8.2.0. Released v3.4.0.
% Domain : Topology
% Problem : Compactness of Lim-inf Topology T06
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [BE01] Bancerek & Endou (2001), Compactness of Lim-inf Topolo
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t6_waybel33 [Urb08]
% Status : Theorem
% Rating : 1.00 v3.4.0
% Syntax : Number of formulae : 8861 (1628 unt; 0 def)
% Number of atoms : 54592 (5317 equ)
% Maximal formula atoms : 70 ( 6 avg)
% Number of connectives : 52569 (6838 ~; 278 |;26726 &)
% (1657 <=>;17070 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 587 ( 585 usr; 2 prp; 0-6 aty)
% Number of functors : 1135 (1135 usr; 282 con; 0-8 aty)
% Number of variables : 21433 (20328 !;1105 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Bushy version: includes all articles that contribute axioms to the
% Normal 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+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+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+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.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+80.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+159.ax').
include('Axioms/SET007/SET007+170.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+207.ax').
include('Axioms/SET007/SET007+210.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+225.ax').
include('Axioms/SET007/SET007+227.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+256.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+301.ax').
include('Axioms/SET007/SET007+309.ax').
include('Axioms/SET007/SET007+317.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+354.ax').
include('Axioms/SET007/SET007+387.ax').
include('Axioms/SET007/SET007+426.ax').
include('Axioms/SET007/SET007+438.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+493.ax').
include('Axioms/SET007/SET007+497.ax').
include('Axioms/SET007/SET007+498.ax').
include('Axioms/SET007/SET007+500.ax').
include('Axioms/SET007/SET007+505.ax').
include('Axioms/SET007/SET007+506.ax').
include('Axioms/SET007/SET007+538.ax').
include('Axioms/SET007/SET007+542.ax').
include('Axioms/SET007/SET007+544.ax').
include('Axioms/SET007/SET007+558.ax').
include('Axioms/SET007/SET007+560.ax').
include('Axioms/SET007/SET007+572.ax').
include('Axioms/SET007/SET007+573.ax').
include('Axioms/SET007/SET007+586.ax').
include('Axioms/SET007/SET007+636.ax').
include('Axioms/SET007/SET007+637.ax').
include('Axioms/SET007/SET007+655.ax').
include('Axioms/SET007/SET007+695.ax').
%------------------------------------------------------------------------------
fof(dt_k1_waybel33,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ( v1_waybel_9(k2_waybel33(A))
& m1_yellow_9(k2_waybel33(A),A) ) ) ).
fof(d1_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v2_waybel_0(C,k3_yellow_1(B))
& v13_waybel_0(C,k3_yellow_1(B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) )
=> k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) ).
fof(t1_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(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))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& v2_waybel_0(E,k3_yellow_1(C))
& v13_waybel_0(E,k3_yellow_1(C))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& v2_waybel_0(F,k3_yellow_1(D))
& v13_waybel_0(F,k3_yellow_1(D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_yellow_1(D)))) )
=> ( E = F
=> k1_waybel33(A,C,E) = k1_waybel33(B,D,F) ) ) ) ) ) ) ) ) ).
fof(d2_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_waybel_9(A) )
=> ( v1_waybel33(A)
<=> u1_pre_topc(A) = k4_waybel28(A) ) ) ).
fof(cc1_waybel33,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v1_waybel33(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A) ) ) ) ).
fof(cc2_waybel33,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel33(A) ) ) ) ).
fof(rc1_waybel33,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_waybel33(A) ) ).
fof(t2_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( l1_waybel_0(C,A)
=> ? [D] :
( v6_waybel_0(D,B)
& l1_waybel_0(D,B)
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) ).
fof(t3_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [C] :
( l1_waybel_0(C,A)
=> ~ ( r2_hidden(C,k7_yellow_6(A))
& ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v6_waybel_0(D,B)
& v7_waybel_0(D)
& l1_waybel_0(D,B) )
=> ~ ( r2_hidden(D,k7_yellow_6(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) ) ) ) ) ) ) ) ).
fof(l6_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [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,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( E = F
=> r1_tarski(a_3_2_waybel33(A,C,E),a_3_2_waybel33(B,D,F)) ) ) ) ) ) ) ) ) ).
fof(l7_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v25_waybel_0(B)
& v2_lattice3(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))
=> ! [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,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> r1_tarski(a_2_1_waybel33(A,C),a_2_1_waybel33(B,D)) ) ) ) ) ) ) ).
fof(t4_waybel33,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v2_lattice3(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))
=> ! [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,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> k1_waybel11(A,C) = k1_waybel11(B,D) ) ) ) ) ) ) ).
fof(t5_waybel33,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ( u1_struct_0(A) = u1_struct_0(B)
=> ! [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,B) )
=> ( ( g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(A,C) = u1_waybel_0(B,D) )
=> ! [E] :
( m2_yellow_6(E,A,C)
=> ? [F] :
( v6_waybel_0(F,B)
& m2_yellow_6(F,B,D)
& g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(F),u1_orders_2(F))
& u1_waybel_0(A,E) = u1_waybel_0(B,F) ) ) ) ) ) ) ) ) ).
fof(t6_waybel33,conjecture,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v2_lattice3(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))
=> ! [C] :
( l1_waybel_0(C,A)
=> ! [D] :
~ ( r2_hidden(k4_tarski(C,D),k3_waybel28(A))
& ! [E] :
( ( ~ v3_struct_0(E)
& v3_orders_2(E)
& v6_waybel_0(E,B)
& v7_waybel_0(E)
& l1_waybel_0(E,B) )
=> ~ ( r2_hidden(k4_tarski(E,D),k3_waybel28(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(E),u1_orders_2(E))
& u1_waybel_0(A,C) = u1_waybel_0(B,E) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------