TPTP Problem File: LAT300+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LAT300+3 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Ideals T24
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Ban96] Bancerek (1996), Ideals
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t24_filter_2 [Urb08]
% Status : Theorem
% Rating : 0.75 v8.2.0, 0.78 v8.1.0, 0.81 v7.5.0, 0.88 v7.4.0, 0.87 v7.3.0, 0.90 v7.1.0, 0.87 v7.0.0, 0.80 v6.4.0, 0.77 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.87 v5.5.0, 0.93 v5.3.0, 0.96 v5.2.0, 0.90 v5.0.0, 0.92 v4.1.0, 0.96 v3.7.0, 1.00 v3.4.0
% Syntax : Number of formulae : 13607 (2726 unt; 0 def)
% Number of atoms : 84432 (9472 equ)
% Maximal formula atoms : 52 ( 6 avg)
% Number of connectives : 81474 (10649 ~; 462 |;40446 &)
% (2326 <=>;27591 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 773 ( 771 usr; 2 prp; 0-6 aty)
% Number of functors : 1970 (1970 usr; 510 con; 0-10 aty)
% Number of variables : 33816 (32214 !;1602 ?)
% 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').
%------------------------------------------------------------------------------
fof(dt_m1_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_2(B,A)
=> ( ~ v1_xboole_0(B)
& m2_lattice4(B,A) ) ) ) ).
fof(existence_m1_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] : m1_filter_2(B,A) ) ).
fof(redefinition_m1_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_filter_2(B,A)
<=> m1_filter_0(B,A) ) ) ).
fof(dt_m2_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ~ v1_xboole_0(B)
& m2_lattice4(B,A) ) ) ) ).
fof(existence_m2_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] : m2_filter_2(B,A) ) ).
fof(symmetry_r1_filter_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ( r1_filter_2(A,B,C)
=> r1_filter_2(A,C,B) ) ) ).
fof(reflexivity_r1_filter_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> r1_filter_2(A,B,B) ) ).
fof(redefinition_r1_filter_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ( r1_filter_2(A,B,C)
<=> B = C ) ) ).
fof(dt_k1_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> m1_filter_2(k1_filter_2(A),A) ) ).
fof(redefinition_k1_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k1_filter_2(A) = k1_filter_0(A) ) ).
fof(dt_k2_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_filter_2(k2_filter_2(A,B),A) ) ).
fof(redefinition_k2_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k2_filter_2(A,B) = k2_filter_0(A,B) ) ).
fof(dt_k3_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_filter_2(k3_filter_2(A,B),A) ) ).
fof(redefinition_k3_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_filter_2(A,B) = k3_filter_0(A,B) ) ).
fof(dt_k4_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> m1_filter_2(k4_filter_2(A,B,C),A) ) ).
fof(redefinition_k4_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A)
& m1_filter_0(C,A) )
=> k4_filter_2(A,B,C) = k5_filter_0(A,B,C) ) ).
fof(dt_k5_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A))) ) ).
fof(dt_k6_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(k1_lattice2(A))) )
=> m1_subset_1(k6_filter_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k7_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) ) ).
fof(dt_k8_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) )
=> m1_subset_1(k8_filter_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k9_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_lattice4(B,A) )
=> m2_lattice4(k9_filter_2(A,B),k1_lattice2(A)) ) ).
fof(redefinition_k9_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_lattice4(B,A) )
=> k9_filter_2(A,B) = k7_filter_2(A,B) ) ).
fof(dt_k10_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
=> ( ~ v1_xboole_0(k10_filter_2(A,B))
& m2_lattice4(k10_filter_2(A,B),k1_lattice2(A)) ) ) ).
fof(redefinition_k10_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
=> k10_filter_2(A,B) = k7_filter_2(A,B) ) ).
fof(dt_k11_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_lattice4(B,k1_lattice2(A)) )
=> m2_lattice4(k11_filter_2(A,B),A) ) ).
fof(redefinition_k11_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_lattice4(B,k1_lattice2(A)) )
=> k11_filter_2(A,B) = k8_filter_2(A,B) ) ).
fof(dt_k12_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m2_lattice4(B,k1_lattice2(A)) )
=> ( ~ v1_xboole_0(k12_filter_2(A,B))
& m2_lattice4(k12_filter_2(A,B),A) ) ) ).
fof(redefinition_k12_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m2_lattice4(B,k1_lattice2(A)) )
=> k12_filter_2(A,B) = k8_filter_2(A,B) ) ).
fof(dt_k13_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> m2_filter_2(k13_filter_2(A,B),k1_lattice2(A)) ) ).
fof(redefinition_k13_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,A) )
=> k13_filter_2(A,B) = k7_filter_2(A,B) ) ).
fof(dt_k14_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,k1_lattice2(A)) )
=> m2_filter_2(k14_filter_2(A,B),A) ) ).
fof(redefinition_k14_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_filter_0(B,k1_lattice2(A)) )
=> k14_filter_2(A,B) = k8_filter_2(A,B) ) ).
fof(dt_k15_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,A) )
=> m1_filter_2(k15_filter_2(A,B),k1_lattice2(A)) ) ).
fof(redefinition_k15_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,A) )
=> k15_filter_2(A,B) = k7_filter_2(A,B) ) ).
fof(dt_k16_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,k1_lattice2(A)) )
=> m1_filter_2(k16_filter_2(A,B),A) ) ).
fof(redefinition_k16_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,k1_lattice2(A)) )
=> k16_filter_2(A,B) = k8_filter_2(A,B) ) ).
fof(dt_k17_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> m2_filter_2(k17_filter_2(A),A) ) ).
fof(dt_k18_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m2_filter_2(k18_filter_2(A,B),A) ) ).
fof(dt_k19_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m2_filter_2(k19_filter_2(A,B),A) ) ).
fof(dt_k20_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k20_filter_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k21_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,A)
& m2_filter_2(C,A) )
=> m2_filter_2(k21_filter_2(A,B,C),A) ) ).
fof(redefinition_k21_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(A)
& m2_filter_2(B,A)
& m2_filter_2(C,A) )
=> k21_filter_2(A,B,C) = k20_filter_2(A,B,C) ) ).
fof(dt_k22_filter_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k22_filter_2(A,B,C))
& m2_lattice4(k22_filter_2(A,B,C),A) ) ) ).
fof(dt_k23_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
=> m2_nat_lat(k23_filter_2(A,B),A) ) ).
fof(dt_k24_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_nat_lat(B,A) )
=> ( v3_lattices(k24_filter_2(A,B))
& m2_nat_lat(k24_filter_2(A,B),k1_lattice2(A)) ) ) ).
fof(redefinition_k24_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m2_nat_lat(B,A) )
=> k24_filter_2(A,B) = k1_lattice2(B) ) ).
fof(t1_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ( D = k1_realset1(C,B)
=> ( ( v1_binop_1(C,A)
=> v1_binop_1(D,B) )
& ( v3_binop_1(C,A)
=> v3_binop_1(D,B) )
& ( v2_binop_1(C,A)
=> v2_binop_1(D,B) ) ) ) ) ) ) ) ).
fof(t2_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m2_subset_1(F,A,B)
=> ( ( D = k1_realset1(C,B)
& F = E )
=> ( ( r1_binop_1(A,E,C)
=> r1_binop_1(B,F,D) )
& ( r2_binop_1(A,E,C)
=> r2_binop_1(B,F,D) )
& ( r3_binop_1(A,E,C)
=> r3_binop_1(B,F,D) ) ) ) ) ) ) ) ) ) ).
fof(t3_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ( ( E = k1_realset1(C,B)
& F = k1_realset1(D,B) )
=> ( ( r4_binop_1(A,C,D)
=> r4_binop_1(B,E,F) )
& ( r5_binop_1(A,C,D)
=> r5_binop_1(B,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t4_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ( ( E = k1_realset1(C,B)
& F = k1_realset1(D,B)
& r6_binop_1(A,C,D) )
=> r6_binop_1(B,E,F) ) ) ) ) ) ) ) ).
fof(t5_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ( ( E = k1_realset1(C,B)
& F = k1_realset1(D,B)
& r1_lattice2(A,C,D) )
=> r1_lattice2(B,E,F) ) ) ) ) ) ) ) ).
fof(d1_filter_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ( r1_filter_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,B)
<=> r2_hidden(D,C) ) ) ) ) ) ) ).
fof(t6_filter_2,axiom,
! [A] :
( l3_lattices(A)
=> ! [B] :
( l3_lattices(B)
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> k1_lattice2(A) = k1_lattice2(B) ) ) ) ).
fof(t7_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k1_lattice2(k1_lattice2(A)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ).
fof(t8_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(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))
=> ( ( C = E
& D = F )
=> ( k1_lattices(A,C,D) = k1_lattices(B,E,F)
& k2_lattices(A,C,D) = k2_lattices(B,E,F)
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v13_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> k5_lattices(A) = k5_lattices(B) ) ) ) ).
fof(t10_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v14_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v14_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> k6_lattices(A) = k6_lattices(B) ) ) ) ).
fof(t11_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v15_lattices(B)
& v16_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(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))
=> ( ( C = E
& D = F
& r2_lattices(A,C,D) )
=> r2_lattices(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t12_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& v17_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k7_lattices(A,C) = k7_lattices(B,D) ) ) ) ) ) ) ).
fof(t13_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
<=> r2_hidden(k4_lattices(A,C,D),B) ) ) )
=> m2_lattice4(B,A) ) ) ) ).
fof(t14_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
<=> r2_hidden(k3_lattices(A,C,D),B) ) ) )
=> m2_lattice4(B,A) ) ) ) ).
fof(d2_filter_2,axiom,
$true ).
fof(d3_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_lattice4(B,A) )
=> ( m2_filter_2(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
<=> r2_hidden(k3_lattices(A,C,D),B) ) ) ) ) ) ) ).
fof(t15_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
<=> r2_hidden(k3_lattices(A,C,D),B) ) ) )
=> m2_filter_2(B,A) ) ) ) ).
fof(t16_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> ! [C] :
( m1_filter_2(C,A)
=> m1_filter_2(C,B) ) ) ) ) ).
fof(t17_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
=> ! [C] :
( m2_filter_2(C,A)
=> m2_filter_2(C,B) ) ) ) ) ).
fof(d4_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_filter_2(A,B) = B ) ) ).
fof(d5_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_lattice2(A)))
=> k6_filter_2(A,B) = B ) ) ).
fof(t18_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_lattice2(A)))
=> ( k6_filter_2(A,k5_filter_2(A,B)) = B
& k5_filter_2(A,k6_filter_2(A,C)) = C ) ) ) ) ).
fof(t19_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_lattice2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
=> ( k4_lattices(A,B,C) = k3_lattices(k1_lattice2(A),k5_filter_2(A,B),k5_filter_2(A,C))
& k3_lattices(A,B,C) = k4_lattices(k1_lattice2(A),k5_filter_2(A,B),k5_filter_2(A,C))
& k4_lattices(k1_lattice2(A),D,E) = k3_lattices(A,k6_filter_2(A,D),k6_filter_2(A,E))
& k3_lattices(k1_lattice2(A),D,E) = k4_lattices(A,k6_filter_2(A,D),k6_filter_2(A,E)) ) ) ) ) ) ) ).
fof(t20_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_lattice2(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_lattice2(A)))
=> ( ( r3_lattices(A,B,C)
=> r3_lattices(k1_lattice2(A),k5_filter_2(A,C),k5_filter_2(A,B)) )
& ( r3_lattices(k1_lattice2(A),k5_filter_2(A,C),k5_filter_2(A,B))
=> r3_lattices(A,B,C) )
& ( r3_lattices(k1_lattice2(A),D,E)
=> r3_lattices(A,k6_filter_2(A,E),k6_filter_2(A,D)) )
& ( r3_lattices(A,k6_filter_2(A,E),k6_filter_2(A,D))
=> r3_lattices(k1_lattice2(A),D,E) ) ) ) ) ) ) ) ).
fof(t21_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_filter_2(B,A)
<=> m1_filter_2(B,k1_lattice2(A)) ) ) ).
fof(d6_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k7_filter_2(A,B) = B ) ) ).
fof(d7_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
=> k8_filter_2(A,B) = B ) ) ).
fof(fc1_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ v1_xboole_0(k7_filter_2(A,B)) ) ).
fof(fc2_filter_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) )
=> ~ v1_xboole_0(k8_filter_2(A,B)) ) ).
fof(t22_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( m2_filter_2(B,A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k3_lattices(A,C,D),B) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r3_lattices(A,D,C) )
=> r2_hidden(D,B) ) ) ) ) ) ) ) ).
fof(t23_filter_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_filter_2(D,A)
=> ( r2_hidden(B,D)
=> ( r2_hidden(k4_lattices(A,B,C),D)
& r2_hidden(k4_lattices(A,C,B),D) ) ) ) ) ) ) ).
fof(t24_filter_2,conjecture,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,B) ) ) ) ).
%------------------------------------------------------------------------------