TPTP Problem File: LAT347+2.p
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%------------------------------------------------------------------------------
% File : LAT347+2 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Representation Theorem for Free Continuous Lattices T01
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Rud96] Rudnicki (1998), Representation Theorem for Free Conti
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t1_waybel22 [Urb08]
% Status : Theorem
% Rating : 0.83 v8.2.0, 0.89 v7.5.0, 0.91 v7.4.0, 0.93 v7.1.0, 0.96 v7.0.0, 0.97 v6.4.0, 0.96 v6.1.0, 0.97 v6.0.0, 0.96 v5.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 8950 (1780 unt; 0 def)
% Number of atoms : 51702 (6105 equ)
% Maximal formula atoms : 62 ( 5 avg)
% Number of connectives : 48251 (5499 ~; 316 |;23904 &)
% (1571 <=>;16961 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 657 ( 655 usr; 1 prp; 0-6 aty)
% Number of functors : 1505 (1505 usr; 443 con; 0-10 aty)
% Number of variables : 21962 (20833 !;1129 ?)
% 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+21.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+34.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.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+67.ax').
include('Axioms/SET007/SET007+68.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+159.ax').
include('Axioms/SET007/SET007+182.ax').
include('Axioms/SET007/SET007+188.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+210.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+237.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+311.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+363.ax').
include('Axioms/SET007/SET007+393.ax').
include('Axioms/SET007/SET007+396.ax').
include('Axioms/SET007/SET007+412.ax').
include('Axioms/SET007/SET007+427.ax').
include('Axioms/SET007/SET007+449.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+489.ax').
include('Axioms/SET007/SET007+490.ax').
include('Axioms/SET007/SET007+494.ax').
include('Axioms/SET007/SET007+495.ax').
include('Axioms/SET007/SET007+498.ax').
include('Axioms/SET007/SET007+505.ax').
include('Axioms/SET007/SET007+509.ax').
include('Axioms/SET007/SET007+520.ax').
include('Axioms/SET007/SET007+527.ax').
include('Axioms/SET007/SET007+537.ax').
include('Axioms/SET007/SET007+538.ax').
include('Axioms/SET007/SET007+559.ax').
%------------------------------------------------------------------------------
fof(dt_k1_waybel22,axiom,
! [A] : m1_subset_1(k1_waybel22(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_yellow_1(A))))) ).
fof(dt_k2_waybel22,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,k1_waybel22(A),u1_struct_0(B))
& m1_relset_1(C,k1_waybel22(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_waybel22(A,B,C))
& v1_funct_2(k2_waybel22(A,B,C),u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B))
& m2_relset_1(k2_waybel22(A,B,C),u1_struct_0(k2_yellow_1(k9_waybel_0(k3_yellow_1(A)))),u1_struct_0(B)) ) ) ).
fof(l1_waybel22,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] :
( r1_tarski(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_yellow_0(A,k3_tarski(B)) = k2_yellow_0(A,a_2_2_waybel22(A,B)) ) ) ).
fof(l2_waybel22,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] :
( r1_tarski(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_yellow_0(A,k3_tarski(B)) = k1_yellow_0(A,a_2_4_waybel22(A,B)) ) ) ).
fof(t1_waybel22,conjecture,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k2_yellow_1(k9_waybel_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k9_waybel_0(A))))) )
=> k1_yellow_0(k2_yellow_1(k9_waybel_0(A)),B) = k3_tarski(B) ) ) ).
%------------------------------------------------------------------------------